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Chapter 3: Q. 391 (page 407)

The measures of two angles of a triangle are 22and85 degrees. Find the measure of the third angle.

Short Answer

Expert verified

The measure of the third angle is73掳.

Step by step solution

01

Step 1. Given Information   

The measure of two angles are22and85and we have to find the measure of the third angle.

02

Step 2. Translate into an equation

Let xbe the measure of the third angle.

The sum of the angle of a triangle is 180掳.

So, the equation isrole="math" localid="1647264130553" 22掳+85掳+x=180掳

03

Step 3. Solve the equation

By proceeding with the equation we get,

22掳+85掳+x=180掳105掳+x=180掳x=180掳-107掳x=73掳

Thus, the measure of the third angle is73degree.

04

Step 4. Check the answer

To check the answer substitute the angle 73in the formula of the sum of a triangle.

22掳+85掳+73掳=180掳180掳=180掳

It is true.

Thus, the measure of the third angle is 73掳.22掳+85掳+73掳=180掳180掳=180掳

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