William W. answered • 03/12/25
Tutor
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Experienced Tutor and Retired Engineer
∠D subtends arc ABC therefore the measure of arc ABC is 2•m∠D = 2•125° = 250°. That means the measure of arc ADC is 360° - 250° or 110°.
Since ∠B subtends arc ADC then m∠B = (1/2)(110) so:
(1/2)y = (1/2)(110)
(1/2)y = 55
y = 110
Likewise, ∠A subtends arc DCB therefore arc DCB = 210° which means arc DAB = 360° - 210° = 150°.
Since ∠C subtends arc DAB then m∠C = (1/2)(150°) = 75° so:
(1/3)x = 75
x = 225
As a check, polygon ABCD is a quadrilateral therefore the sum of its internal angles is 360°.
m∠A + m∠B + m∠C + m∠D = 360
105 + 55 + 75 + 125 = 360
360 = 360 so we can be assured we have the correct answers.
