Chapter 10: Q.14 (page 539)

Explain why the sum of the measures of the acute angles of a right triangle is $90 °$ .

Short Answer

Expert verified

The sum of the measures of the acute angle of a right triangle is $90 °$ .

Step by step solution

Step 1. Given Information.

A right-angled triangle.

Step 2. Formula.

Sum of all angles of a triangle is $180 °$ .

Step 3. Explanation.

The sum of all the angles of a triangle is $180 °$ .

Let x be the measure of first acute angle of the triangle.

Let y be the measure of second acute angle of the triangle.

Calculate the sum of all the angles.

$x + y + 90 {}^{\circ}= 180 °$

Now, subtract 90 from both the sides.

$x + y + 90 {}^{\circ}- 90 {}^{\circ}= 180 {}^{\circ}- 90 °$

This gives us-

$x + y = 90 °$

Step 4. Conclusion.

Hence, successfully proven that the sum of acute angles of a right-angles triangle is equal to $90 °$ .

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Explain why the sum of the measures of the acute angles of a right triangle is $90 °$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formula.

Step 3. Explanation.

Step 4. Conclusion.

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Explain why the sum of the measures of the acute angles of a right triangle is90°.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Formula.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Explain why the sum of the measures of the acute angles of a right triangle is $90 °$ .