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QuestionThe supplement of ∠A\angle A is 129∘129^{\circ}. Find the complement of ∠A\angle A. Options: 39∘39^{\circ}, 51∘51^{\circ}, 90∘90^{\circ}, 129∘129^{\circ}.

Studdy Solution

STEP 1

Assumptions1. The supplement of ∠A\angle A is 129∘129^{\circ}. . We need to find the complement of ∠A\angle A.

STEP 2

First, we need to understand what the terms "supplement" and "complement" mean in the context of angles.The supplement of an angle is what, when added to the angle, equals 180∘180^{\circ}. The complement of an angle is what, when added to the angle, equals 90∘90^{\circ}.

STEP 3

Given that the supplement of ∠A\angle A is 129∘129^{\circ}, we can find the measure of ∠A\angle A by subtracting the supplement from 180∘180^{\circ}.
∠A=180∘−Supplement of ∠A\angle A =180^{\circ} - Supplement\, of\, \angle A

STEP 4

Plug in the given value for the supplement of ∠A\angle A to calculate the angle.
∠A=180∘−129∘\angle A =180^{\circ} -129^{\circ}

STEP 5

Calculate the measure of ∠A\angle A.
∠A=180∘−129∘=51∘\angle A =180^{\circ} -129^{\circ} =51^{\circ}

STEP 6

Now that we have the measure of ∠A\angle A, we can find the complement of ∠A\angle A by subtracting ∠A\angle A from 90∘90^{\circ}.
Complement of ∠A=90∘−∠AComplement\, of\, \angle A =90^{\circ} - \angle A

STEP 7

Plug in the value for ∠A\angle A to calculate the complement of ∠A\angle A.
Complement of ∠A=90∘−51∘Complement\, of\, \angle A =90^{\circ} -51^{\circ}

STEP 8

Calculate the complement of ∠A\angle A.
Complement of ∠A=90∘−51∘=39∘Complement\, of\, \angle A =90^{\circ} -51^{\circ} =39^{\circ}The complement of ∠A\angle A is 39∘39^{\circ}.

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