Question

Let trapezoid GHIJ be inscribed in⊙Q. If the measure of arc HI is 82°, and the measure of arc JI is 77°, calculate (m∠HKI).

a) 123 degrees

b) 103 degrees

c) 118 degrees

d) 100 degrees

Answer 1

To find the measure of angle HKI, subtract the measures of arcs HI and JI from 360°.

Step-by-step explanation:

To find the measure of angle HKI, we need to consider the central angles that intersect this angle. From the given information, we know that arc HI measures 82° and arc JI measures 77°. Since angle HKI is formed by arcs HI and JI, we can find its measure by subtracting the measures of these arcs from 360°, since the sum of the measures of the central angles in a circle is always 360°.

Therefore, angle HKI = 360° - (82° + 77°) = 360° - 159° = 201°