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)  

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.

can you add an image ?

step-by-step explanation: