Homework 1: Introduction to Angles

For the given angle (diagram 1),

a) name the vertex ​ (a)   ,

b) name the sides = ​ (b)   ,

c) name the angle three ways: ​​ (c)  

d) classify the angle: ​ (d)  

• Y
• X
• YZ,YX
• XZ,ZY
• <YXZ, <XZY,<Z
• Straight
• Right
• <Y,<XYZ,<ZYX

For the given angle (diagram 2), a) name the vertex, b) name the sides, c) name the angle three ways, and d) classify the angle.

• a) M

  b) LM, MN

  c) ∠LMN, ∠NML, ∠M

  d) Acute angle

• a) L

  b) LM, LN

  c) ∠LMN, ∠NML, ∠L

  d) Right angle

• a) N

  b) MN, NL

  c) ∠LMN, ∠NML, ∠N

  d) Obtuse angle

• a) M

  b) LM, MN

  c) ∠LMN, ∠NML, ∠L

  d) Acute angle

For the given angle (diagram 3), a) name the vertex, b) name the sides, c) name the angle three ways, and d) classify the angle.

• a) V

  b) SV, CV

  c) ∠SVC, ∠CVS, ∠V

  d) Right angle

• a) S

  b) SV, SC

  c) ∠SVC, ∠CSV, ∠S

  d) Acute angle

• a) C

  b) CV, CS

  c) ∠VCS, ∠SCV, ∠C

  d) Right angle

• a) C

  b) VS, VC

  c) ∠VSC, ∠CVS, ∠V

  d) Straight angle

If m∠P = (7x – 22)° and ∠P is a right angle, the value of x is:

• 12

• 14

• 16

• 18

If m∠A = (5x + 45)° and ∠A is a straight angle, the value of x is:

• 27

• 29

• 31

• 33

The measure of ∠N is (15x + 47)°. If x = 8, what is the measure of ∠N?

• 167°

• 120°

• 175°

• 200°

The measure of ∠H is (11x – 29)°. If x = 19, what is the measure of ∠H?

• 180°

• 120°

• 180°

• 180°

If m∠J = (7x + 13)°, m∠K = (83 – 2x)°, and the sum of the measures of the angles is 141°, find the measure of each angle. (Give the measure of ∠J and ∠K.)

• m∠J = 62°, m∠K = 79°

• m∠J = 59°, m∠K = 82°

• m∠J = 65°, m∠K = 76°

• m∠J = 70°, m∠K = 71°

If m∠T = (2x + 85)°, m∠V = (5x + 29)°, and the sum of the measures of the angles is 93°, find the measure of each angle.

• m∠T = 87°, m∠V = 6°

• m∠T = 12°, m∠V = 81°

• m∠T = 45°, m∠V = 48°

• m∠T = 60°, m∠V = 33°

If m∠Y = (2x – 3)°, m∠Z = (13x – 41)°, and ∠Z is a straight angle, find the sum of the measures of the two angles.

• The sum of the measures is 180° (since a straight angle is 180°).

• The sum of the measures is 90°.

• The sum of the measures is 120°.

• The sum of the measures is 360°.