Question

a. p
b. s
c. q
d. r
unit 8: circle geometry

1. o is the centre of this circle and point m is a point of tangency.

determine the value of ( x^circ ).
a. ( 37^circ )
b. ( 53^circ )
c. ( 143^circ )
d. ( 90^circ )
questions i should practice:

Explanation:

Step1: Recall tangent-radius property

A tangent to a circle is perpendicular to the radius at the point of tangency. So, \( \angle OMN = 90^\circ \).

Step2: Use triangle angle sum

In \( \triangle OMN \), the sum of angles is \( 180^\circ \). We know \( \angle MON = 37^\circ \) and \( \angle OMN = 90^\circ \). So, \( x = 180^\circ - 90^\circ - 37^\circ \).
\( x = 53^\circ \)

Answer:

b. \( 53^\circ \)