Question

What is the measure of angle DQM?

Answer 1

`40` degrees

Explanation:

Triangle DQM has angles 90 (right angle), 50 (given) and `angle DQM`
Using triangle sum of 180, `angle DQM=40`

Answer 2

`D\hat{Q}M = 40°`

Explanation:

The tangent to a circle always forms an angle of `90°` with the radius. So, the triangle `MDQ` is a right triangle, where `M\hat{D}Q` is the right angle.

Moreover, we know that `D\hat{M}Q` is `50°`.

Since we know that the sum of the inner angles of any triangle is `180°`, we have

`M\hat{D}Q+D\hat{M}Q+D\hat{Q}M = 90+50+D\hat{Q}M = 180`

and we can deduce

`D\hat{Q}M = 180-90-50 = 90-50=40`