Question

the measure of an angle is 51.7°. what is the measure of its complementary angle?

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). Let the given angle be \(\theta = 51.7^{\circ}\) and its complementary angle be \(\alpha\). Then \(\theta+\alpha = 90^{\circ}\).

Step2: Solve for the complementary angle

We can find \(\alpha\) by subtracting \(\theta\) from \(90^{\circ}\). So \(\alpha=90^{\circ}-\theta\). Substitute \(\theta = 51.7^{\circ}\) into the formula: \(\alpha = 90^{\circ}- 51.7^{\circ}\).

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Answer:

\(38.3^{\circ}\)