When two lines cross at a single point, a linear pair of angles is generated. The measure of ∠B is 36° while the measure of ∠A is 144°.
What is the Linear Pair?
When two lines cross at a single point, a linear pair of angles is generated. If the angles are next to each other after the two lines intersect, they are considered to be linear. A linear pair's sum of angles is always 180 degrees.
As we know that the sum of a linear pair is always 180°, therefore, the sum of the two of the given angles ∠A and ∠B can be written as,
[tex]\angle A + \angle B = 180^o\\\\[/tex]
As we know that the measure of ∠A is 4∠B, therefore,
[tex]4\angle B + \angle B = 180^o\\\\5\angle B = 180^o\\\\\angle B = 36^o[/tex]
Now, as we know that the measure of ∠B is 36°, therefore, the measure of ∠A can be written as,
∠A = 4∠B
∠A = 4 × 36° = 144°
Hence, the measure of ∠B is 36° while the measure of ∠A is 144°.
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