Chapter 3: Q. 391 (page 407)

The measures of two angles of a triangle are $22 and 85$ degrees. Find the measure of the third angle.

Short Answer

Expert verified

The measure of the third angle is $73 ° .$

Step by step solution

Step 1. Given Information

The measure of two angles are $22 and 85$ and we have to find the measure of the third angle.

Step 2. Translate into an equation

Let xbe the measure of the third angle.

The sum of the angle of a triangle is $180 ° .$

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

Step 3. Solve the equation

By proceeding with the equation we get,

$22 ° + 85 ° + x = 180 ° 105 ° + x = 180 ° x = 180 ° - 107 ° x = 73 °$

Thus, the measure of the third angle is $73$ degree.

Step 4. Check the answer

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

$22 ° + 85 ° + 73 ° = 180 ° 180 ° = 180 °$

It is true.

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

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The measures of two angles of a triangle are $22 and 85$ degrees. Find the measure of the third angle.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Translate into an equation

Step 3. Solve the equation

Step 4. Check the answer

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Translate into an equation

Step 3. Solve the equation

Step 4. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

The measures of two angles of a triangle are $22 and 85$ degrees. Find the measure of the third angle.