Question

Line ab intersects line cd at point f. Line ab intersects line cd at point f, with a ray fe forming a right angle efb. If m∠afc = (9x − 3)° and m∠bfd = (6x 9)°, what is m∠afc?

Option 1: 4°
Option 2: 33°
Option 3: 45°
Option 4: 66°

Answer 1

Given the intersection of two lines and the angles m∠afc and m∠bfd, we can solve for the value of m∠afc. In this case, m∠afc is found to be 33° by setting up an equation with the given angles and solving for x.

Step-by-step explanation:

Given that line ab intersects line cd at point f, with ray fe forming a right angle efb, and the angles m∠afc and m∠bfd are given as (9x - 3)° and (6x + 9)° respectively, we need to find the value of m∠afc.

Since angle efb is a right angle, m∠afd + m∠bfd = 90°. Therefore, (9x - 3) + (6x + 9) = 90. Simplifying this equation, we get 15x + 6 = 90. Solving for x, we find x = 4.

Substituting the value of x back into m∠afc, we get m∠afc = (9(4) - 3)° = 33°.