Since ∠A and ∠B forms a straight line, ∠A and ∠B are a linear pair.
Linear pair:
A linear pair is the sum of two angles that forms a straight line (180°).
⇒ ∠A + ∠B = 180°
Measure of ∠A:
Subtract the measure of ∠B from 180 to determine the measure of ∠A.
⇒ ∠A = 180 - ∠B
Measure of ∠B:
Subtract the measure of ∠A from 180 to determine the measure of ∠B.
⇒ ∠B = 180 - ∠A
*Let us take a few examples to understand the concept better.
Example (Given measure of ∠B):
Let the measure of ∠B (In the triangle shown) be 105°.
What is the measure of ∠A?
Solution:
Substitute the measure of ∠B in the equation ∠A = 180 - ∠B:
- ⇒ ∠A = 180 - ∠B
- ⇒ ∠A = 180 - 105
Simplify the equation:
- ⇒ ∠A = 180 - 105
- ⇒ ∠A = 75°
Therefore, the measure of ∠A is 75°.
Example (Given measure of ∠A):
Let the measure of ∠A (In the triangle shown) be 60°.
What is the measure of ∠B?
Solution:
Substitute the measure of ∠A in the equation ∠B = 180 - ∠A:
- ⇒ ∠B = 180 - ∠A
- ⇒ ∠B = 180 - 60
Simplify the equation:
- ⇒ ∠B = 180 - 60
- ⇒ ∠B = 120°
Therefore, the measure of ∠B is 120°.
Learn more about linear pairs: https://brainly.com/question/26555759
