QQuestionMathematics
QuestionMathematics
# What is the measure of ∠C?
- A. 60°
- B. 30°
- C. 90°
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Answer
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Step 1:: Identify the given information and the goal.
The given information is that ∠A and ∠B are complementary angles, and the measure of ∠A is 30°. The goal is to find the measure of ∠C.
Step 2:: Understand complementary angles.
Complementary angles are two angles whose sum is 90 degrees.
Step 3:: Use the given information to find the measure of ∠B.
Since ∠A and ∠B are complementary, we have: ∠A + ∠B = 90° Given that ∠A = 30°, we can substitute this value into the equation: 30° + ∠B = 90° Now, solve for ∠B: ∠B = 90° - 30° = 60°
Step 4:: Analyze the triangle to find the measure of ∠C.
In the given triangle, we now know that ∠A = 30°, ∠B = 60°. Since the sum of the angles in a triangle is always 180°, we can find the measure of ∠C as follows: ∠C = 180° - (∠A + ∠B) Substitute the known values: ∠C = 180° - (30° + 60°) Calculate the sum inside the parentheses: ∠C = 180° - 90° Finally, find the measure of ∠C: ∠C = 90°
Final Answer
The measure of ∠C is 90° (option C).
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