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Angles-practice-1

Angles Practice 1

  • To convert degrees to radians, multiply the degree measure by  \frac{\pi radians}{180^{0}}.

Example:

Convert 85° to radians:

Solution

85^{^{0}}=85(\frac{\\\pi radians}{180^{0}})=\frac{17\pi }{36}

  • To convert from radians to degrees, multiply the radian measure by \frac{180^{0}}{\pi radians}.

Example

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

Solution

\frac{\pi }{6}=\left ( \frac{\pi radians}{6} \right )\left (\frac{180^{0}}{\pi radians} \right )=30^{^{0}}

1. In the figure below, angles 3m and 4n are vertical angles. What is the value of m in terms of n?

Angles-Practice-1-Pict1

(A) n

(B) 12n

(C) \frac{n}{12}

(D) \frac{3n}{4}

(E) \frac{4n}{3}

Solution

The two angles are vertical angles, so their measures are equal:

3m = 4n

To solve for m, divide both sides by 3:

m=\frac{4n}{3}

Thus, the right answer is (E)

2. In the figure below, v = 3u. What is the value of w?

Angles-Practice-1-Pict2

(A) 15

(B) 30

(C) 45

(D) 60

(E) 75

Solution

Angles u and v are supplementary angles because they complete a line, so u + v = 180.

Substitute 3u for v into this equation and solve for u:

u + 3u = 180

4u = 180

u = 45

The two angles u and w are vertical angles, so they’re equal. Thus, w = 45, and the right answer is (C) .

3. In the following diagram, angle 1 is equal to 40°, and angle 2 is equal to 150°. What is the number of degrees in angle 3?

Angles-Practice-1-Pict3

(A) 70°

(B) 90°

(C) 110°

(D) 190°

(E) The answer cannot be determined from the given information.

Solution

Choice C is correct. In the problem it is given that ∠1 = 40° and ∠2 = 150°. The diagram below makes it apparent that:

(1) ∠1 = ∠4 and ∠3 = ∠5 (vertical angles);

(2) ∠6 + ∠2 = 180° (straight angle);

(3) ∠4 + ∠5 + ∠6 = 180° (sum of angles in a triangle).

To solve the problem, ∠3 must be related through the above information to the known quantities in ∠1 and ∠2.

Proceed as follows:

∠3 = ∠5, but ∠5 = 180° – ∠4 – ∠6.

∠4 = ∠1 = 40° and ∠6 = 180° – ∠2 = 180° – 150° = 30°.

Therefore, ∠3 = 180° – 40° – 30° = 110°.

Angles-Practice-1-Pict3-solution

4. In the figure below, angles p and q are complementary, with 2p = 3q. What is the measure of angle p?

Angles-Practice-1-Pict4
Solution

The problem states that angles p and q are complementary, so you have two equations to work with:

p + q = 90

2p = 3q

Solve the top equation for q:

q = 90 – p

Now substitute 90 – p for q in the second equation and solve for p:

2p = 3(90 – p)

2p = 270 – 3p

5p = 270

p = 54

Therefore, the answer is

————End of Angles Practice 1————



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