Q: Which of the following is the correct formula to convert degrees to radians?

$$\text{radians} = \text{degrees} \times \frac{\pi}{180}$$

Question 1

Which of the following best describes an angle in standard position?

Accepted Answer

Its vertex is at the origin and its initial side lies along the positive x-axis.

Question 2

If an angle measures $$-60^\circ$$, in which direction is it measured from the positive x-axis?

Accepted Answer

Clockwise

Question 3

Which of the following angles is an obtuse angle?

Accepted Answer

$$120^\circ$$

Question 4

What is the complement of a $$37^\circ$$ angle?

Accepted Answer

$$53^\circ$$

Question 5

What is the supplement of a $$110^\circ$$ angle?

Accepted Answer

$$70^\circ$$

Question 6

If two angles are complementary and one angle measures $$x$$, what is the measure of the other angle?

Accepted Answer

$$90^\circ - x$$

Question 7

If two angles are supplementary and one angle measures $$x$$, what is the measure of the other angle?

Accepted Answer

$$180^\circ - x$$

Question 8

A right triangle has one angle measuring $$35^\circ. $$What is the measure of the other non-right angle?

Accepted Answer

$$55^\circ$$

Question 9

Convert $$120^\circ to $$radians.

Accepted Answer

$$\frac{2\pi}{3}$$

Question 10

Convert $$\frac{5\pi}{6}$$ radians to degrees.

Accepted Answer

$$150^\circ$$

Question 11

Which of the following is true about complementary angles?

Accepted Answer

Their measures add up to $$90^\circ.$$

Question 12

Which of the following is true about supplementary angles?

Accepted Answer

Their measures add up to $$180^\circ.$$

Question 13

A straight angle is equivalent to which of the following?

Accepted Answer

$$180^\circ$$

Question 14

If $$\angle ABC$$ and $$\angle CBD$$ are supplementary and $$\angle ABC = 2x + 10^\circ$$, $$\angle CBD = 3x - 20^\circ$$, what is the value of $$x$$?

Accepted Answer

$$38$$

Question 15

Which of the following angles is a right angle?

Accepted Answer

$$90^\circ$$

Question 16

A surveyor measures an angle of $$225^\circ$$ from the positive x-axis. In which quadrant does the terminal side of the angle lie?

Accepted Answer

Third quadrant

Question 17

Which of the following is the radian measure for a full circle?

Accepted Answer

$$2\pi$$

Question 18

If an angle in standard position has its terminal side on the negative y-axis, what is its degree measure?

Accepted Answer

$$270^\circ$$

Question 19

A clock shows the time as 3:00. What is the angle between the hour and minute hands?

Accepted Answer

$$90^\circ$$

Question 20

Which of the following is the correct formula to convert degrees to radians?

Accepted Answer

$$	ext{radians} = 	ext{degrees} 	imes \frac{\pi}{180}$$

Measuring Angles: Standard Position, Types, Complementary & Supplementary Angles, and Radian Conversion

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