Problem: Write an article based on this summary: Draw the polygon whose angles you need to sum. Choose one vertex. Draw a straight line from Point A to each other vertex in the polygon. Multiply the number of triangles you created by 180.

Answer: The polygon can have any number of sides and can be regular or irregular. For example, you might want to find the sum of the interior angles of a hexagon, so you would draw a six-sided shape. Label this vertex A. A vertex is a point where two sides of a polygon meet. The lines should not cross. You should create a number of triangles.  You do not have to draw lines to the adjacent vertices, since they are already connected by a side. For example, for a hexagon you should draw three lines, dividing the shape into 4 triangles. Since there are 180 degrees in a triangle, by multiplying the number of triangles in your polygon by 180, you can find the sum of the interior angles of your polygon. For example, since you divided your hexagon into 4 triangles, you would calculate 4×180=720{\displaystyle 4\times 180=720} to find a total of 720 degrees in the interior of your polygon.


Problem: Write an article based on this summary: Talk about actions happening in the present. Use the preterite tense for completed past actions. Try the imperfect tense for habitual actions. Move to the conditional tense if the action depends on something else. Form the future tense by adding the appropriate ending.

Answer: The present tense is used for anything that's currently happening. To conjugate an -er verb in the present tense, remove the -er ending from the infinitive and add -o, -es, -e, -emos, -éis, or -en, depending on the subject pronoun.   Yo como: I eat.  Tú comes: You [informal] eat.  Él/ella/usted come: He/she eats; you [formal] eat.  Nosotros comemos: We eat.  Vosotros coméis: You all [informal] eat.  Ellos/ellas/ustedes comen: They/you all [formal] eat. If you want to talk about something that happened completely in the past, remove the -er ending from the infinitive of your verb and add the appropriate ending. Depending on your subject pronoun, your ending will be -í, -iste, -ió, -imos, -isteis, or -ieron.   Yo comí: I ate.  Tú comiste: You [informal] ate.  Él/ella/usted comió: He/she/you [formal] ate.  Nosotros comimos: We ate.  Vosotros comisteis: You [informal] ate.  Ellos/ellas/ustedes comieron: They/you [formal] ate. If an action occurred in the past but continues into the present, the imperfect tense is more accurate than the preterite tense. This tense is also appropriate if you "were doing" something, but were interrupted. To conjugate -er verbs in this tense, replace the -er ending with -ía, ías, ía, -íamos, íais, or -ían.   Yo comía: I was eating.  Tú comías: You [informal] were eating.  Él/ella/usted comía: He/she was eating; you [formal] were eating.  Nosotros comíamos: We were eating.  Vosotros comíais: You all [informal] were eating.  Ellos/ellas/ustedes comían: They/you all [formal] were eating. If you want to talk about a hypothetical situation, or something that will only occur if something else takes place first, use the conditional tense. To conjugate -er verbs, you'll use the same endings that you used for the imperfect tense. However, you'll attach them to the end of the infinitive, rather than removing the -er ending.   Yo comería: I would eat [if].  Tú comerías: You [informal] would eat [if].  Él/ella/usted comería: He/she/you [formal] would eat [if].  Nosotros comeríamos: We would eat [if].  Vosotros comeríais: You all [informal] would eat [if].  Ellos/ellas/ustedes comerían: They/you all [formal] would eat [if]. Like the conditional tense, verbs are conjugated in simple future tense by adding an ending directly onto the end of the infinitive. Depending on the subject pronoun, you'll add -é, -ás, -á, -emos, -éis, or -án.   Yo comeré: I will eat.  Tú comerás: You [informal] will eat.  Él/ella/usted comerá: He/she/you [formal] will eat.  Nosotros comerermos: We will eat.  Vosotros comeréis: You all [informal] will eat.  Ellos/ellas/ustedes comerán: They/you all [formal] will eat.


Problem: Write an article based on this summary: Pick a large number. Plug your number, which we'll call x, into this formula to calculate pi:

Answer: The bigger the number, the more accurate your calculation will be. x * sin(180 / x). For this to work, make sure your calculator is set to Degrees. The reason this is called a Limit is because the result of it is 'limited' to pi. As you increase your number x, the result will get closer and closer to the value of pi.


Problem: Write an article based on this summary: Clean your lacquered brass piece. Remove the lacquer with hot water. Remove the lacquer with varnish remover. Polish the brass. Consider polishing your brass with commercial cleaners. Consider alternative brass cleaners. Protect your brass from future tarnish.

Answer:
The first line of defense for keeping your brass pieces clean is to regularly dust them using a soft rag. After dusting your lacquered brass, dip a soft cotton cloth into a mixture of mild dish detergent and lukewarm water.  Wring out the cloth so it's only slightly damp, and gently wipe the brass surface clean. Once you have cleaned the surface, use a wrung out cloth dipped in clean water to remove any remaining soap, and then dry the brass piece thoroughly. If you are trying to remove tarnish that has accumulated underneath lacquered brass, you need to remove the layer of lacquer first. Hot water softens the lacquer layering covering brass. Place the brass piece in a sink basin, and pour hot water over the brass. The hot water will heat up the brass, making it expand. The lacquer will expand with the brass. However, when the brass starts to cool down, it will slightly shrink, but the lacquer won't shrink with it. Once the brass is cool, the lacquer should be slightly separated from the brass surface, and can easily be peeled away. You could also try boiling your brass in water to remove the lacquer, depending on the size of the piece. All you need to do is immerse the brass piece in a non-aluminum pot with boiling water, and let it sit for a few minutes. Then, carefully take the brass piece out of the water, let it cool, and peel off the lacquer. Place the brass piece on a table that is heavily layered with newspapers. The newspaper will help protect the workspace by absorbing any varnish remover drippings. Consider using a paintbrush to thoroughly and evenly coat the brass piece with the varnish remover. Once you have applied the remover, let it sit for a minute or two, and then wipe away the varnish remover with a soft cloth. Be sure to consult the instructions found on the container of varnish remover.  Be cautious and follow the manufacturer's cleaning guidelines, because varnish remover is made from strong chemicals that could be dangerous. Protect your skin and wear rubber gloves when handling varnish remover. Because of the hazardous fumes from varnish remover, work outside or in an area that's well ventilated. Also stay away from open flames when working with varnish remover since it's highly flammable. Make sure the brass is clean of all surface dust and dirt before you begin polishing. There are many kinds of commercial brass polishes, but you can make your own brass polish at home with lemon. Cut a lemon in half and squeeze all the juice from the half lemon into a small bowl. Add in either table salt or baking soda – it doesn't matter which, the salt/baking soda is only acting as an abrasive – until you form a paste. This might require about a teaspoon or more of salt or baking soda. Apply the paste to the brass piece using a soft cloth.  Make sure you apply the paste going with the grain of the metal. If not, you could make tiny little scratches in the brass surface. Don't rub the paste too harshly into the brass piece. The abrasive salt/baking soda will gently remove the tarnish. Consider using a soft-bristled toothbrush to clean the nooks and hard to reach areas of your brass piece. There are many eco-friendly brass cleaners that remove tarnish and restore shine to brass pieces without scratching and damaging the surface.  Sometimes, brass cleansers have an abrasive element in their formula, so be mindful to not damage fragile etchings on your brass piece.  Stay way from muriatic acid. It does not properly clean brass, and can leave behind permanent stains.  Undiluted white vinegar or ammonia can be highly effective in cleaning antique brass. Allow the brass piece to soak for an hour in either vinegar or ammonia. Both products are natural cleaning agents, and can give brass a lasting, shiny finish. Although you can make your own brass cleaner at home or use commercial brass cleaners bought from the store, consider using some of these other natural ingredients to clean your brass pieces:   Ketchup. Use a soft cloth to slather your brass piece with ketchup. Let the ketchup sit on the brass surface for approximately 10 minutes, and then wipe the ketchup off with a clean, damp cloth. Dry the brass piece thoroughly.   Yogurt. Cover your brass piece with plain yogurt. The lactic acid in the yogurt is what works to break down and dissolve the tarnishing on the brass. Allow the yogurt to dry on the brass, and then rinse it off with water, and dry the brass piece with a clean cloth.   White vinegar and salt. Cover the brass piece with white vinegar (either by pouring or spraying the vinegar over the brass surface), and then sprinkle salt over the vinegar. Wet a cloth with a little bit of vinegar, and gently wipe down the brass. Dry with a clean  cloth. After you're finished cleaning your brass piece, protect it from future tarnishing by applying a lacquered finish. You can apply the lacquer using either a paintbrush or a cotton ball. Consult the instructions on the lacquer container to see the manufacturer's suggestions.  However you decide to apply the lacquer, be sure to only put on a thin layer. Watch for any dripping lacquer, because the drippings can dry, leaving your brass piece covered in drip streaks.  Allow the brass piece to dry thoroughly before touching. After the lacquer is dry, wipe the brass with a clean cloth to give it some shine.