Question

In circle A, tangent FH and chord EG intersect to form angle HEG. FInd the measure of angle HEG.

A. 36 degrees
B. 72 degrees
C. 144 degrees
D. 216 degrees

Answer 1

B.

Explanation:

Answer 2

Option B is correct, i.e. 72 degrees.

Explanation:

Given is a diagram of circle in which tangent-chord angle is formed i.e. angle ∠HEG.

We can find the angle ∠HEG using the Tangent-Chord Angle formula as follows:-

Tangent-chord angle = Half of intercepted arc.

angle ∠HEG = 1/2 arcEG.

(3x + 18) = 1/2 * (9x - 18)

6x + 36 = 9x - 18

9x - 6x = 36 + 18

3x = 54

x = 18.

angle ∠HEG = 3x+18 = 3*18 + 18 = 72 degrees.

Hence, option B is correct, i.e. 72 degrees.