If arc sq = 84° and ∠rps = 26°, what is the measure of arc rs?

Solution:

Given, arc sq = 84°

∠rps = 26°

We have to find the measure of arc rs.

We know that the measurement of the external angle is the semi-difference of the arcs.

From the figure,

∠rps is the external angle.

So, ∠rps = \(\frac{1}{2}\)(arc rs - arc sq)

Now, 26° = \(\frac{1}{2}\)(arc rs - 84°)

52° = arc rs - 84°

arc rs = 84° + 52°

arc rs = 136°

Therefore, the measure of arc rs is 136°.

Summary:

If arc sq = 84° and ∠rps = 26°, the measure of arc rs is 136°.

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