Question

Which statement can be used to solve for the measure of angle a?

Question 12 options:

a = 180° + 77° + 60°


a = 180° - 90° - 77°


a = 77° - 60°


a = 180° - 60° - 77°

Answer 1

To solve for the measure of angle a, let's evaluate each option:

1.
`\displaystyle\sf a = 180^(\circ) + 77^(\circ) + 60^(\circ)`

Calculating the sum, we have
`\displaystyle\sf a = 317^(\circ)`

2.
`\displaystyle\sf a = 180^(\circ) - 90^(\circ) - 77^(\circ)`

Calculating the difference, we have
`\displaystyle\sf a = 13^(\circ)`

3.
`\displaystyle\sf a = 77^(\circ) - 60^(\circ)`

Calculating the difference, we have
`\displaystyle\sf a = 17^(\circ)`

4.
`\displaystyle\sf a = 180^(\circ) - 60^(\circ) - 77^(\circ)`

Calculating the difference, we have
`\displaystyle\sf a = 43^(\circ)`

Based on the given options, the correct equation to solve for the measure of angle a is option 3:
`\displaystyle\sf a = 77^(\circ) - 60^(\circ)`. Therefore, the measure of angle a is
`\displaystyle\sf 17^(\circ)`.

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