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Dmitrij [34]
3 years ago
6

Pls help (9th honors geo - circles)

Mathematics
1 answer:
Mariana [72]3 years ago
6 0

• Angles DXC and AXB form a vertical pair, so they are congruent and have the same measure.

• ∆ABD is isosceles, since it's given that AD and BD are congruent. This means the "base angles" BAD and ABD have the same measure; call this measure <em>x</em>.

• The measure of angle ADB can be computed by using the inscribed angle theorem, which says

m∠ADB = 1/2 (100°) = 50°

(that is, it's half the measure of the subtended arc AB whose measure is 100°)

• The interior angle to any triangle sum to 180° in measure. So we have in ∆ABD,

m∠ADB + 2<em>x</em> = 180°

Solve for <em>x</em> :

50° + 2<em>x</em> = 180°

2<em>x</em> = 130°

<em>x</em> = 65°

• Use the inscribed angle theorem again to find the measure of angle BAC. This will be half the measure of the subtended arc BC, so

m∠BAC = 1/2 (50°) = 25°

• Now in ∆ABX, we have

m∠AXB + 25° + 65° = 180°

m∠AXB = 90°

Hence m∠DXC = 90°.

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