Applying the definition of linear pairs, the measure of angle BOC formed by the two intersecting lines is: C. 50°.
What are Linear Pairs?
When two lines intersect each other at a point, the set of angle pairs that lie adjacent to each other on a straight line are called linear pairs, and their sum is equal to 180 degrees.
Given that lines AC and BD meet at point O, as shown in the diagram below, angles AOB and BOC are a linear pair sharing a common side BO.
Therefore:
m∠AOB + m∠BOC = 180° [supplementary angles]
Substitute
6x - 14 + 2x + 2 = 180
Combine like terms
8x - 12 = 180
8x = 180 + 12 [addition property of equality]
8x = 192
Divide both sides by 8
8x/8 = 192/8
x = 24
Find the measure of angle BOC by substituting the value of x:
m∠BOC = 2x + 2 = 2(24) + 2
m∠BOC = 48 + 2
m∠BOC = 50°
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