# What is the measure of angle DQM?

May 16, 2018

$40$ degrees

#### Explanation:

Triangle DQM has angles 90 (right angle), 50 (given) and $\angle D Q M$
Using triangle sum of 180, $\angle D Q M = 40$

May 16, 2018

D\hat{Q}M = 40°

#### Explanation:

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

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

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

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

and we can deduce

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