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
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