William W. answered • 03/12/25
Tutor
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Experienced Tutor and Retired Engineer
∠B subtends arc ADC therefore the measure of arc ADC is 2•m∠B = 2•40° = 80°. That means the measure of arc ABC is 360° - 80° or 280°.
Since ∠D subtends arc ABC then m∠D = (1/2)(280) so:
(1/3)x - 10 = (1/2)(280)
(1/3)x - 10 = 140
(1/3)x = 150
x = 450
Likewise, ∠A subtends arc DCB therefore arc DCB = 240° which means arc DAB = 360° - 240° = 120°.
Since ∠C subtends arc DAB then m∠C = (1/2)(120°) = 60° so:
4y = 60
y = 15
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
120 + 40 + 60 + 140 = 360
360 = 360 so we can be assured we have the correct answers.
