Qa is tangent to circle m at point d and the m angle qmd=40 what is the measure of angle mqa?

∠MQA = 130°

Step-by-step explanation:

∠MDQ = 90° ( angle between tangent and radius )

Given ∠QMD = 40°, then

∠MQD = 180° - (90 + 40)° = 180° - 130° = 50° ( sum of angles in a triangle )

∠MQD and ∠MQA form a straight angle and are supplementary, thus

∠MQA = 180° - 50° = 130°

OR

The external angle of a triangle is equal to the sum of the 2 opposite interior angles

∠MQA is an exterior angle of the triangle, thus

∠MQA = 90° + 40° = 130°