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Chapter 7: Q27. (page 244)

Find the measure of each angle.

The measures of the acute angles of a right triangle are in the ratio5:7.

Short Answer

Expert verified

The measures of each angle is90鈭�,37鈰�5鈭� and52鈰�5鈭� .

Step by step solution

01

Step 1. Given information.

The ratio between acute angles of a right triangle is,

5:7

02

Step 2. Concept used.

The sum of angles of a triangle is180鈭�.

And, one angle of a right triangle is90鈭�90鈭�.

Since, ratio of the angles is always in the simplified form,

It might not represent the actual measure.

03

Step 3. Considering the angles as5x and7x .

The sum of the angles of the triangle can be expressed using the above relation as,

5x+7x=9012x=90x=7.5

So, each of the angles are given by,

5x=5脳7鈰�55x=37.5

And,

7x=7脳7鈰�57x=52.5

Therefore, the angles of right triangle are90鈭�,37鈰�5鈭� and 52鈰�5鈭�.

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