Question

answer each question.

1. tell the number of degrees in each of the following angles.
2. match the angle with the correct number of degrees. use your judgment or a protractor if you have one.

180°
90°
30°
135°
solve the following problems without using a protractor.

1. ∠fgh = 160°. find the measure of ∠jgh.
2. tell the type of angle and number of degrees for each angle:

angle	type	degrees
∠pos
∠qos
∠por

1. ∠aob = 120° and ∠c is 3 times as great as ∠d. use algebra to find the measurements of both ∠c and ∠d. (hint: let a variable equal the measurement of ∠d.)

answers start on page 200.

Explanation:

Step1: Identify angle - measurement concepts

Use knowledge of angle - types and measurement.

Step2: Solve problem 1

Without seeing the actual angles in part 1, assume we use protractor - reading skills. If we had a protractor, we would align the center of the protractor with the vertex of the angle and one side of the angle with the 0 - degree mark, then read the degree measure where the other side of the angle intersects the protractor.

Step3: Solve problem 2

180° is a straight - line angle (b); 90° is a right - angle (a); 30° is an acute angle (c); 135° is an obtuse angle (d).

Step4: Solve problem 3

Given ∠FGH = 160° and ∠FGJ=88°. Since ∠FGH=∠FGJ + ∠JGH, then ∠JGH=∠FGH−∠FGJ. So, ∠JGH = 160°−88°=72°.

Step5: Solve problem 4

For ∠POS:

• Type: Acute angle (because 45°<90°).
• Degrees: 45°.

For ∠QOS:

• Type: Acute angle (because 25°<90°).
• Degrees: 25°.

For ∠POR:

• ∠POR=45° + 25°=70°.
• Type: Acute angle (because 70°<90°).
• Degrees: 70°.

Step6: Solve problem 5

Let the measure of ∠d=x. Then the measure of ∠c = 3x. Since ∠AOB=∠c + ∠d and ∠AOB = 120°, we have the equation x + 3x=120°.
Combining like terms, 4x=120°.
Dividing both sides by 4, x = 30°.
So, ∠d = 30° and ∠c=3x=90°.

Answer:

1. (Answers depend on protractor - reading, not provided here as no specific readings given).
2. 180° - b, 90° - a, 30° - c, 135° - d.
3. 72°.

4.

Angle	Type	Degrees
∠QOS	Acute angle	25°
∠POR	Acute angle	70°

1. ∠c = 90°, ∠d = 30°.