Question

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

Answer 1

Answer:

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

Step-by-step 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.