Question

What is the measure of arc WX in the diagram below ?

Answer 1

Your answer would be 45

Answer 2

The measure of the arc WX is 26 degrees.

What is the secant of the circle?

A secant is a line that intersects a circle in exactly two pints. When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one half the positive difference of the measure of the intercepted arcs.

According to the given question.

WSX is a secant angle.

TR and WX are intercepted arcs.

Therefore, by the secant of the circle formula

$\frac{1}{2} (116^{o} -WX) = 45^{o}$

$\implies 116^{o} -WX = 90^{o}$

$\implies WX = 116^{o} -90^{o}\\ \implies WX = 26^{o}$

Hence, the measure of the arc WX is 26 degrees.

Thus, option B is correct.

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