Question

Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.

A. What is the value of x?

B. What is the measure of ∠2?

C. Find the measure of ∠3.

Answer 1

Answer:

• A) x = 18, B) ∠2 = 68°, C) ∠3 = 112°

Step-by-step explanation:

According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.

Given

• ∠2 = 4x-4 and ∠4 = x+50

A) Find the value of x:

• 4x - 4 = x + 50
• 4x - x = 50 + 4
• 3x = 54
• x = 54/3
• x = 18

B) Find the measure of angle 2:

• ∠2 = 4*18 - 4 = 72 - 4 = 68

C) Angles 2 and 3 are supplementary so their sum is 180°.

• ∠2 + ∠3 = 180
• 68 + ∠3 = 180
• ∠3 = 180 - 68
• ∠3 = 112°