Question

NO LINKS!! URGENT HELP PLEASE!!

Find the measure of the arc or angle indicated. for #10, 11, & 12​

Answer 1

10. 114

11. 45

12. 50

Explanation:

10. ∠M = 1/2 arc LN (which is semicircle) = 1/2 (180) = 90

∠N = 180 - 90 - 33 = 57

∠N = 1/2 arc LM => LM = 2 ∠N = 2 x 57 = 114

11. ∠F = 1/2 arc HG => arc HG = 2 x ∠F = 2 x 94 = 188

arc HF = 360 - 188 - 127 = 45

12. ∠D 1/2 arc CE (which is semicircle) = 1/2 (180) = 90

∠E = 1/2 arc CD = 80/2 = 40

∠C = 180 - 90 - 40 = 50

Answer 2

10) 114°

11) 45°

12) 50°

Explanation:

You want the angles or arcs shown in the figures with inscribed angles and triangles.

Inscribed angle

The measure of an inscribed angle is half the measure of the arc it subtends. Conversely, the the measure of the subtended arc is twice the measure of the inscribed angle.

Arcs

The measure of the arcs of a circle is 360°. The measure of the arc of a semicircle is 180°.

An angle that is inscribed in a semicircle has a measure of 180°/2 = 90°.

10)

Arc LMN is 180°. Arc MN is twice 33°, so ...

arc LM = 180° -2(33°) = 114°

Note that arc LM is also double the inscribed angle MNL, which is the complement of 33°.

11)

Long arc HG is double the measure of the 94° inscribed angle. The remaining unknown arc is the difference between 360° and the two known arcs:

arc HF = 360° -arc HG -arc GF

arc HF = 360° -2(94°) -127° = 45°

12)

Arc CDE is a semicircle, so is 180°. Arc DE is the difference between that and arc CD:

arc DE = 180° -arc CD = 180° -80° = 100°

Inscribed angle C is half this measure:

angle C = (100°)/2 = 50°

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