Question

What are the measures of angles 1 and 2?

Answer 1

In this question we have to use the formula:

$Angle \ formed \ by \ two \ chords = \frac{1}{2}(Sum \ of \ intercepted \ arcs)$

Substituting the values of the intercepted arcs in the formula, we will get

$\angle 1 = \frac{1}{2} (53 + 47) = \frac{1}{2} (100) = 50 degree$

And angles 1 and 2 are linear pair.

So we will get

$\angle 1 + \angle 2 = 180$

Substituting the value of angle 1, we will get

$50 + \angle 2 = 180 \\ \angle 2 = 130 degree$

Answer 2

<1 = 1/2(53+47) = 1/2(100) = 50
<2 = 1/2(360 - 53 - 47) = 1/2(260) = 130