Question

PQ is tangent to the circle at C. In the circle, m (The figure is not drawn to scale.)

Answer 1

Answer:

65°

Step-by-step explanation:

From the figure we can see a circle.

It is given that, measure of arc AD = 80°  therefore m<ACD = 80/2 = 40°

Also m<D = 75°

To find the measure of <DCQ

We know that, an angle made by a tangent and chord is equal to the angle made by the angle made by the chord on other side of the circle.

Here m<DCQ = m<CAD

By using angle sum property,

m<CAD + m<ACD + m<D = 180

m<CAD + 40 + 75 = 180

m<CAD + 115 = 180

m<CAD = 180 - 115 = 65°

Therefore m<DCQ = m< CAD = 65°

The correct answer is third option.