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Chapter 2: Q 545. (page 217)

The measure of the smallest angle in a right triangle is 45掳less than the measure of the next larger angle. Find the measures of all three angles.

Short Answer

Expert verified

Angles are equal to67.5掳,22.5掳,90掳.

Step by step solution

01

Step 1. Given information

The measure of the smallest angle in a right triangle is 45掳less than the measure of the next larger angle.

02

Step 2. Find all the angles of a triangle.

Let the larger angle be x.

Measure of the smallest angle localid="1645120774456" =x-45

Sum of all the angles of a triangle is equal to 180掳.

x+x-45掳+90掳=180掳2x=135掳x=67.5掳

Measure of the smallest angle=x-45掳

=67.5掳-45掳=22.5掳

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