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Please help quickly

Please help quickly-example-1

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In the figure angle x and y are

1. x = 90 degrees and y = 65 degrees

2. x = 160 degrees and y = 80 degrees

3. z = 160 degrees

x = 175 degrees

y = 130 degrees

How to find the values of x and y

1. angle x = 90 degrees (angle on a semicircle)

assuming angle C is 25 degrees

25 + y = 90 degrees (complementary angle)

y = 90 - 25

y = 65 degrees

2. y = 80 degrees (angles are intercepting equal arc)

x = 80 * 2 (intercepted arc measure = inscribed angle * 2)

x = 160 degrees

3. z = 80 * 2 (intercepted arc measure = inscribed angle * 2)

z = 160 degrees

x = HKJ / 2 (intercepted arc measure = inscribed angle * 2)

HKJ = 360 - 50 - z (sum of angles of a circle)

HKJ = 360 - 50 - 160

HKJ = 150

therefore, x = 150 / 2 = 75 degrees

y = 360 - 80 - 75 - x (sum of angles of a quadrilateral)

y = 360 - 80 - 75 - 75

y = 360 - 230

y = 130 degrees

User Jacob Dalton
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