Question

QA is tangent to circle M at point D and the m angle QMD=40 what is the measure of angle MQA?

Answer 1

∠MQA = 130°

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°

Answer 2

the answer is MQA =130°

Wen u draw a parallel line with respect to MD through Q, the angle between the line become 40 degree - alternate angles

so the rest is 90 degree, therefore 90 + 40 = 130 degree