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SVETLANKA909090 [29]
3 years ago
11

Help me please I’m having trouble with it

Mathematics
1 answer:
gavmur [86]3 years ago
4 0

Given:

Measure of arcs 50°, 115° and 85°

To find:

The measure of the numbered angle 5.

Solution:

Let the missing arc measure be A.

The arc measure of a full circle is 360°

m(ar A) + 50° + 115° + 85° = 360°

m(ar A) + 250° = 360°

Subtract 250 from both sides.

m(ar A) = 110°

<em>If two chords intersects inside a circle, then the measure of the angle formed is half of the sum of intercepted arcs.</em>

$\Rightarrow m\angle 5 =\frac{1}{2} (110^\circ+115^\circ)

$\Rightarrow m\angle 5 =\frac{1}{2} (225^\circ)

$\Rightarrow m\angle 5 =112.5^\circ

The measure of the numbered angle is 112.5°.

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