Question

practice worksheet
name:
date:
class:
a: identify the angle type (a–d).
(angle a diagram: acute angle)
(angle b diagram: right angle)
(angle c diagram: obtuse angle)
(angle d diagram: straight angle)

1. ∠a:
2. ∠b:
3. ∠c:
4. ∠d:

part b: complementary/supplementary & vertical angles

1. ∠p and ∠q are complementary. if m∠p = 37°, find m∠q
2. ∠r and ∠s are supplementary. if m∠r = 108°, find m∠s
3. in diagram e (intersecting lines with one angle 50°), vertical angles are equal. if one angle is 50°, find x =
4. in triangle f (angles 45°, 65°, and x°), find the missing angle x

(diagram g: a transversal with a 70° angle)

1. in diagram g, given the 70° angle...

Explanation:

Let's solve the problems one by one:

Part A: Identify the angle type

1. ∠A: The angle is less than 90°, so it's an Acute angle.
2. ∠B: The angle is 90° (right angle symbol), so it's a Right angle.
3. ∠C: The angle is greater than 90° but less than 180°, so it's an Obtuse angle.
4. ∠D: The angle is a straight line (180°), so it's a Straight angle.

Part B: Complementary/Supplementary & Vertical Angles

1. ∠P and ∠Q are complementary (sum to 90°).

Given \( m\angle P = 37^\circ \),
\( m\angle Q = 90^\circ - 37^\circ = 53^\circ \).

1. ∠R and ∠S are supplementary (sum to 180°).

Given \( m\angle R = 108^\circ \),
\( m\angle S = 180^\circ - 108^\circ = 72^\circ \).

1. Vertical angles are equal (diagram E).

If one angle is \( 50^\circ \), then \( x = 50^\circ \) (vertical angles are congruent).

1. Triangle F: Sum of angles in a triangle is 180°

Given angles: \( 45^\circ \) and \( 65^\circ \),
\( x = 180^\circ - 45^\circ - 65^\circ = 70^\circ \).

Final Answers (Key Problems):

• ∠Q: \( \boldsymbol{53^\circ} \)
• ∠S: \( \boldsymbol{72^\circ} \)
• \( x \) (diagram E): \( \boldsymbol{50^\circ} \)
• \( x \) (triangle F): \( \boldsymbol{70^\circ} \)

Answer:

Let's solve the problems one by one:

Part A: Identify the angle type

1. ∠A: The angle is less than 90°, so it's an Acute angle.
2. ∠B: The angle is 90° (right angle symbol), so it's a Right angle.
3. ∠C: The angle is greater than 90° but less than 180°, so it's an Obtuse angle.
4. ∠D: The angle is a straight line (180°), so it's a Straight angle.

Part B: Complementary/Supplementary & Vertical Angles

1. ∠P and ∠Q are complementary (sum to 90°).

Given \( m\angle P = 37^\circ \),
\( m\angle Q = 90^\circ - 37^\circ = 53^\circ \).

1. ∠R and ∠S are supplementary (sum to 180°).

Given \( m\angle R = 108^\circ \),
\( m\angle S = 180^\circ - 108^\circ = 72^\circ \).

1. Vertical angles are equal (diagram E).

If one angle is \( 50^\circ \), then \( x = 50^\circ \) (vertical angles are congruent).

1. Triangle F: Sum of angles in a triangle is 180°

Given angles: \( 45^\circ \) and \( 65^\circ \),
\( x = 180^\circ - 45^\circ - 65^\circ = 70^\circ \).

Final Answers (Key Problems):

• ∠Q: \( \boldsymbol{53^\circ} \)
• ∠S: \( \boldsymbol{72^\circ} \)
• \( x \) (diagram E): \( \boldsymbol{50^\circ} \)
• \( x \) (triangle F): \( \boldsymbol{70^\circ} \)