Question

The diagram shown is two intersecting lines. The measure of 5 is 47°.

Answer 1

a. Using the vertical angles theorem, m∠7 = 47°.

b. Based on the definition of linear pair, the equation that can be used to solve for x is: 2x - 5 + 47 = 180.

c. x = 69

What is a Linear Pair?

A linear pair is two angles whose sum equals 180°.

Given the image, where:

m∠5 = 47°

a. ∠5 and ∠7 are vertical angles. Since verticl angles are congurent, therefore:

m∠7 = m∠5 = 47°

m∠7 = 47°

b. m∠6 = (2x - 5)°

m∠6 + m∠5 = 180° (linear pair)

Substitute

2x - 5 + 47 = 180 (equation that can be used to solve x)

c. 2x - 5 + 47 = 180

2x + 42 = 180

2x = 180 - 42

2x = 138

x = 138/2

x = 69

Learn more about linear pair on:

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