Question

The measure of ZBC = 180°, and the length of AD and Date tool, which is the measure of ZACD?

Answer 1

Answer:

B. 45°

Step-by-step explanation:

recall that Thales' theorem states that the diameter of a circle always subtends a right angle on any point on the circle.

what this means is that if ABC is the diameter of the circle, then AD and DC always meet at the circumference at 90°

in this case, if ∠ADC is 90° (by thales theorem), and AD = DC, then we have an isoceles triangle.

This also means that the base angles of the isoceles triangle, ∠DAC and ∠ACD must be equal.

recall that all interior angles of a triangle add up to 180°

180° = ∠ADC + ∠DAC +∠ACD

180° = ∠ADC + 2 ∠ACD

180° = 90° + 2 ∠ACD

2 ∠ACD = 90°

∠ACD = 45°