Question

∠6 and ∠7 form a linear pair. twice the measure of ∠6 is twelve more than four times the measure of ∠7. __________ measure of each angle.

Answer 1

The measure of ∠6 is 72 degrees and the measure of ∠7 is 108 degrees. The two equations derived from the problem, when solved together, yield these values

Step-by-step explanation:

The subject of this question is Mathematics, specifically it deals with the topic of angles. Since ∠6 and ∠7 form a linear pair, they add up to 180 degrees as this is the definition of a linear pair. If twice the measure of ∠6 is twelve more than four times the measure of ∠7, we can denote ∠6 as x and ∠7 as y, the equation will be 2x = 4y + 12. Simultaneously, we consider x + y = 180 because they form a linear pair. Solved together, these equations yield the measures of angles ∠6 and ∠7. By substitution or elimination method, we can find x to be 72 and y to be 108. Therefore, the measure of ∠6 is 72 degrees and ∠7 is 108 degrees.

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