1.given: triangle pqr with m∠p=(2x)° , m∠q=(4x)° , and m∠r=(6x)° . prove: x = 15 by the triangle sum theorem, the sum of the angles in a triangle is equal to 180°. therefore, m∠p+m∠q+m∠r=180° . using the (2x)°+(4x)°+(6x)°=180° . simplifying the equation gets 12x = 180. finally, using the division property of equality, answer to each box to complete substitution property, distributive property, angle addition postulate, x=12 x=15 x=30

we have

m∠P=

m∠Q=

m∠R=

1) By the triangle sum theorem, the sum of the angles in a triangle is equal to

therefore

m∠P+m∠Q+m∠R=

we know that

Substitution Property of Equality, states that If the values of two quantities are known to be equal, you can replace the value of one quantity with the other

so

2) Using the Substitution Property of Equality

Simplifying the equation gets

3) using the division property of equality

The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal

therefore

the answer is

Part a) Substitution Property of Equality

Part b)  

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.