The angle measurements in the diagram are represented by the following expressions

∠A+∠B=180° [Co-exterior angles]

5x-15+2x+21=180°

7x+6=180

7x=180-6

7x=174

x=24.85

∠ B = 45°

Step-by-step explanation:

∠ A and ∠ Bare alternate exterior angles and are congruent , then

5x - 15 = 2x + 21 ( subtract 2x from both sides )

3x - 15 = 21 ( add 15 to both sides )

3x = 36 ( divide both sides by 3 )

x = 12

Then

∠ B = 2x + 21 = 2(12) + 21 = 24 + 21 = 45°

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

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