Question

Drag an answer to each box to complete this paragraph proof.

Given: Triangle PQR with m∠P=(5x)° , m∠Q=(5x)° , and m∠R=(8x)° .
Prove: x = 10

By the triangle sum theorem, the sum of the angles in a triangle is 180°. Therefore, using the given and triangle sum theorem, . 1)__________ Using the substitution property, (5x)°+(5x)°+(8x)°=180° . Simplifying the equation gets 18x = 180. Finally, using the division property of equality, 2)___________

m<P+m<Q+m<R=90 degrees  


m<P+m<Q+m<R=180 degrees
m<P+m<Q+m<R=360 degrees

x=5 x=10 x=18

Answer 1

Just took the test. My answer is in the screenshot below :-)

Answer 2

Given: Triangle PQR with m∠P=(5x)° , m∠Q=(5x)° , and m∠R=(8x)° .

Prove: x = 10

Solution:

By the triangle sum theorem, the sum of the angles in a triangle is 180°. Therefore, using the given and triangle sum theorem,

1.
`m \angle P + m \angle Q + m\angle R = 180^\circ`

Using the substitution property, (5x)°+(5x)°+(8x)°=180° . Simplifying the equation gets 18x = 180. Finally, using the division property of equality,

x =
`(180)/(18)`

x =
`10^\circ`