Since an inscribed angle is half of the arc it intercepts, angle KHI is 37.5 degrees (half of 75). The triangle KHI is equilateral since the trapezoid is isosceles, which makes angle HIK also 37.5 degrees. Since there are 180 degrees in a triangle, this leaves 105 degrees for angle HKI.
3 comments:
Since an inscribed angle is half of the arc it intercepts, angle KHI is 37.5 degrees (half of 75). The triangle KHI is equilateral since the trapezoid is isosceles, which makes angle HIK also 37.5 degrees. Since there are 180 degrees in a triangle, this leaves 105 degrees for angle HKI.
That was Ben's comment...and he is looking forward to the next "math problem of the day".
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