Question

Quadrilateral ABCD is inscribed in a circle. ∠A = 64°, ∠B = (6x + 4)°, ∠C = (9x − 1)°. What is ∠D?

a. 64°
b. 82°
c. 90°
d. 98°
e. 116°

Answer 1

Since we don't have a value for x, we cannot determine the exact measure of ∠D.

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle. Since the sum of the angles of a quadrilateral is 360°, we can write the equation:

∠A + ∠B + ∠C + ∠D = 360°

Substituting the given angle measures:

64° + (6x + 4)° + (9x - 1)° + ∠D = 360°

Simplifying the equation:

10x + 67 + ∠D = 360°

∠D = 360° - 10x - 67°

Since we don't have a value for x, we cannot determine the exact measure of ∠D. Therefore, the correct answer is none of the options provided.