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Nadusha1986 [10]
4 years ago
13

Find the measure x of an angle that is complementary to 83º.A )3B)5C)7D)13​

Mathematics
1 answer:
egoroff_w [7]4 years ago
8 0

Answer:

C:7

Step-by-step explanation:

Complementary is what else to add to equal 90 degrees. 10 is complementary to 80 because 80+10=90. Supplementary is what would equal to 180. Complementary is usually used in an right angle and supplementary in a line.

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What is the measure of SQ?<br><br> 1. 95<br> 2. 190<br> 3. 265<br> 4. 360
Vesnalui [34]

Answer:

The measure of arc SQ is 95° ⇒ (1)

Step-by-step explanation:

  • The measure of any circle is 360°
  • The measure of the subtended arc to an inscribed angle is twice the measure of this angle

In the given circle

∵ S lies on the circumference of the circle

∴ ∠QSR is an inscribed angle

∵ ∠QSR is subtended by arc QR

→ By using the 2nd rule above

∴ m arc QR = 2 × m∠QSR

∵ m∠QSR = 95°

∴ m arc QR = 2 × 95

∴ m arc QR = 190°

→ By using the 1st rule above

∵ m of the circle = m arc QR + m arc SQ + m arc SR

∵ m arc SR = 75° and m arc QR = 190°

→ Substitute them in the equation above

∴ 360 = 190 + m arc SQ + 75

→ Add the like term in the right side

∴ 360 = 265 + m arc QS

→ Subtract 265 from both sides

∵ 360 - 265 = 265 - 265 + m arc SQ

∴ 95° = m arc SQ

∴ The measure of arc SQ is 95°

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