Question

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

Answer 1

Part a) Substitution Property of Equality

Part b) x=15

Explanation:

Given triangle PQR with

`m\angle P=(2x)^(\circ)`

`m\angle Q=(4x)^(\circ)`

`m\angle R=(6x)^(\circ)`

By the triangle sum property, the sum of the angles of a triangle is equal to
`180^(\circ)`

∴ m∠P+m∠Q+m∠R=180°

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

`(2x)^(\circ)+(4x)^(\circ)+(6x)^(\circ)=180^(\circ)`

Simplifying the equation we get

`(12x)^(\circ)=180^(\circ)`

Using the division property of equality

The Division Property of Equality states that division with the same non zero number results that both sides remain equal

`((12x)^(\circ))/(12)=(180^(\circ))/(12)`

`x=15`

Hence, the answer is

Part a) Substitution Property of Equality

Part b) x=15

Answer 2

we have

m∠P=
`(2x)\°`

m∠Q=
`(4x)\°`

m∠R=
`(6x)\°`

1) 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\°`

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

`(2x)\°+(4x)\°+(6x)\°=180\°`

Simplifying the equation gets

`(12x)\°=180\°`

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

`(12x)\°/12=180\°/12`

`x=15\°`

therefore

the answer is

Part a) Substitution Property of Equality

Part b)
`x=15\°`