Question

If mBE=119 and mBKE=93, find mUH.

Answer 1

arc UH = 67°

Explanation:

the measure of a chord- chord angle is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , then

`(1)/(2)` ( BE + UH ) = ∠ BKE , that is

`(1)/(2)` (119 + UH ) = 93° ( multiply both sides by 2 to clear the fraction )

119° + UH = 186° ( subtract 119° from both sides )

UH = 67°

Answer 2

Explanation:

∠HKU = ∠BKE {Vertically opposite angles}

∠HKU = 93°

Angles fromed by insecting chords equals half the sum of intercepting arcs.

`\sf \angle HKU =(1)/(2)(arc \ HU + arc \ BE) \\\\ 93^ \circ = (1)/(2)(arc \ HU + 119)`

93 *2 = arc HU + 119

186 = arc HU + 119

186 - 119 = arc HU

arc HU = 67°