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aniked [119]
3 years ago
10

The measure of an angle is three more than twice its supplement. What is the measure of the angle?

Mathematics
1 answer:
Zinaida [17]3 years ago
7 0

Answer: the angle is 1°+n×120°

1°, 121°, 241°


Step-by-step explanation:

Angles are taken modulo 360°, so 363° = 3°.

Angle plus supplement gives 180°.

Let a be angle, s be supplement of a.

So s = 180-a. Given a = 3 + 2s

a = 3 + 2(180 - a)

a = 3 + 360 - 2a = 363 - 2a


3a = 363° or 3° or 723°

a = 121° or 1° or 241°


a = 1°

s = 179°

2s = 358°

2s+3 = 361° = 1° (modulo 360)


a = 121°

s = 180-121 = 59°

2s = 118°

2s + 3 = 121°, as required.


a = 241°

s = 360+180-241 = 540-241 = 299

2s = 598

2s + 3 = 601 = 241 (modulo 360)


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