Question

What’s the angle it’s looking for ?

Answer 1

Given:

m(ar KN) = 2x + 151

m(ar LN) = 61°

m∠NMK = 2x + 45

To find:

m∠NMK

Solution:

By property of circle:

If a tangent and a secant intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

$\Rightarrow m\angle NMK=\frac{1}{2} (m \ ar(KN) - m\ arLN))$

$\Rightarrow 2x+45=\frac{1}{2} (2x + 151-61)$

$\Rightarrow 2x+45=\frac{1}{2} (2x + 90)$

Multiply by 2 on both sides, we get

$\Rightarrow 2\times (2x+45)=2\times \frac{1}{2} (2x + 90)$

$\Rightarrow 4x+90=2x + 90$

Subtract 90 from both sides.

$\Rightarrow 4x+90-90=2x + 90-90$

$\Rightarrow 4x=2x$

Subtract 2x from both sides.

$\Rightarrow 4x-2x=2x-2x$

$\Rightarrow 2x=0$

$\Rightarrow x=0$

Substitute x= 0 in m∠NMK.

m∠NMK = 2x + 45

              = 2(0) + 45

              = 45

Therefore m∠NMK = 45.