Tangent is a straight line that touches the circle at any point on the curve. The measure of ∠DQM in ΔDQM is 40º.
What is a tangent?
A tangent is a straight line that touches the circle at any point on the curve. And the angle made by the tangent with radius is always 90°.
We know that line AD is the tangent to circle M, and line MD is the radius of the circle, therefore, the measure of ∠ADM is 90°.
Now, In ΔDQM, the measure of ∠DMQ is 50º, while the measure of ∠MDQ is 90º. therefore, the sum of all the angles of the ΔDQM can be written as,
[tex]\angle DQM + \angle MDQ + \angle DMQ = 180^o\\\\\angle DQM + 90^o + 50^o = 180^o\\\\\angle DQM = 180^o -90^o -50^o\\\\\angle DQM = 40^o[/tex]
Hence, the measure of ∠DQM is 40º.
Learn more about Tangent:
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