What are the measures of angles 1 and 2? m∠1 = ° m∠2 = °

Solution:

Given, chord intercepted arc RQ = 53°

Chord intercepted arc ST = 47°

We have to find the measure of angle 1 and angle 2.

By using the geometric property,

The measure of the angle formed by 2 chords that intersect inside the circle is half the sum of the chord’s intercepted arcs.

So, measure of angle 1 = (53° + 47°)/2

= 100°/2

m∠1 = 50°

m∠1 + m∠2 = 180°

50° + m∠2 = 180°

m∠2 = 180° - 50°

m∠2 = 130°

Therefore, m∠1 = 50° and m∠2 = 130°.

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What are the measures of angles 1 and 2? m∠1 = ° m∠2 = °

Summary:

The measures of angles 1 and 2 are m∠1 = 50° and m∠2 = 130°.