Question

Given: m∠TRV = 60°

m∠TRS = (4x)
Prove: x = 30
What is the missing reason in step 3?
A) given definition of linear pair
B) TRS and TRV are a linear pair
C) 60R
D) (4x) w

Answer 1

The goal is to prove x = 30, given that angles TRV and TRS form a linear pair, with m∠TRV being 60 degrees. The missing reason in the proof likely involves the definition of a linear pair, which states that the angles add up to 180 degrees.

Step-by-step explanation:

The question pertains to a proof in geometry where the student is given that m∠TRV is 60° and m∠TRS is 4x degrees. The goal is to prove that x equals 30. To complete the proof, we commonly use the fact that angles forming a linear pair sum up to 180 degrees.

If ∠TRV and ∠TRS are a linear pair, their measures would add up to 180 degrees. We are given m∠TRV = 60°, so the equation would be 60 + 4x = 180. Solving for x, we get 4x = 120 and therefore x = 30.

In step 3 of this proof, the missing reason would likely involve the property of linear pairs, making the correct answer most likely ('A') the definition of a linear pair, as it explains why the two angles add up to 180 degrees, allowing us to solve for x.