The measure of the ∠PQR will be 139. The correct answer is option D.
What is a circumscribed circle?
The circumscribed circle or circumcircle of a polygon in geometry is a circle that passes through each of the polygon's vertices. This circle's circumcenter and circumradius are its center and radius, respectively. The circle is defined as the locus of the point traces around a fixed point called the center and is equidistant from the out trace.
The value of the ∠PQR will be calculated as:- The sum of the angles o and Q will be equal to 180. Calculate the value of x first then calculate the angle PQR.
x + 17 + 6x - 5 = 180
Solve the above equation for the value of x.
7x +12 = 180
7x = 180 - 12
7x = 168
x = 168 / 7 = 24
The angle PQR is,
∠PQR = ( 6 x 24 ) -5
∠PQR = 144 - 5
∠PQR = 139
Therefore, the measure of the ∠PQR will be 139. The correct answer is option D.
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