Multiple Choice
An angle measures . What is the measure of its complement?
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1. Measuring Angles
Complementary and Supplementary Angles
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If and are complementary and congruent, what is the measure of ?
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Verified step by step guidance1
Recall that complementary angles are two angles whose measures add up to 90 degrees. So, if angle 1 and angle 2 are complementary, then \(\text{angle 1} + \text{angle 2} = 90^\circ\).
Since angle 1 and angle 2 are congruent, they have the same measure. Let the measure of each angle be \(x\) degrees. So, \(\text{angle 1} = x\) and \(\text{angle 2} = x\).
Substitute the values into the complementary angle equation: \(x + x = 90^\circ\).
Combine like terms to get \$2x = 90^\circ$.
Solve for \(x\) by dividing both sides of the equation by 2: \(x = \frac{90^\circ}{2}\). This gives the measure of angle 1.
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