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In the diagram below, quadrilateral DEFG is inscribed in circle H. Solve for x and y.

In the diagram below, quadrilateral DEFG is inscribed in circle H. Solve for x and-example-1

1 Answer

6 votes

Answer:

x = 100

y = 44

Explanation:

The interior angles of a quadrilateral add up to 360 degrees, so we know that when all four angles are added together, they need to equal 360.

121 + 111 + x - 31 + 2y - 29 = 360

Additionally, the angles opposite each other equals 180 degrees. This means D + F = 180 degrees, and E + G = 180 degrees.

111 + (x - 31) = 180

Subtract 111 from both sides.

x - 31 = 69

Add 31 to each side

x = 100

Plug in the value for x to check the answer

111 + (100 - 31) = 180

Then, for y, we have the same set up

121 + (2y - 29) = 180

Subtract 121 from both sides

2y - 29 = 59

Add 29 to each side

2y = 88

Divide each side by 2

y = 44

Plug in the value for y to check the answer

121 + (2*44 - 29) = 180

This means that angle F equals 59 degrees and angle G equals 69 degrees.

x = 100

y = 44

answered
User Jon Driscoll
by
8.5k points
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