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Mark against the correct answer:
The two angles of a triangle are complementary. The third angle is

A

`60^(@)`

B

`45^(@)`

C

`36^(@)`

D

`90^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to find the third angle of a triangle when two angles are complementary. Let's go through the steps: ### Step-by-Step Solution: 1. **Understanding Complementary Angles**: - Complementary angles are two angles whose sum is 90 degrees. 2. **Setting Up the Triangle**: - Let's denote the three angles of the triangle as Angle A, Angle B, and Angle C. - According to the problem, we can say that Angle A and Angle C are complementary. Therefore: \[ \text{Angle A} + \text{Angle C} = 90^\circ \] 3. **Using the Triangle Angle Sum Property**: - The sum of all angles in a triangle is always 180 degrees. Hence, we can write: \[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \] 4. **Substituting the Complementary Angles**: - Since we know that Angle A + Angle C = 90 degrees, we can substitute this into the triangle angle sum equation: \[ 90^\circ + \text{Angle B} = 180^\circ \] 5. **Solving for Angle B**: - To find Angle B, we can rearrange the equation: \[ \text{Angle B} = 180^\circ - 90^\circ \] - Simplifying this gives: \[ \text{Angle B} = 90^\circ \] 6. **Conclusion**: - Therefore, the third angle (Angle B) is 90 degrees. ### Final Answer: The third angle is **90 degrees**.
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