Question

1) Which is the measure of ∠A?

A) 93°
B) 113°
C) 138°
D) 180°

2) Which is the measure of ∠C?
A) 42°
B) 138°
C) 180°
D) 218°

3) Which is the measure of ∠B?
A) 42°
B) 138°
C) 180°
D) 218°


4) Find the value of x.
A) 21
B) 27
C) 31
D) 34

5) Find the measure for ∠MQX.
A) 54°
B) 59°
C) 63°
D) 65°

Answer 1

Part 1) Option A) 93°

Part 2) Option B) 138°

Part 3) Option A) 42°

Part 4) Option A) 21

Part 5) Option A) 54°

Explanation:

Part 1) Which is the measure of ∠A?

see the attached figure N 1

we know that

m∠A+87°=180° -----> by supplementary angles (form a linear pair)

so

m∠A=180°-87°=93°

Part 2) Which is the measure of ∠C?

see the attached figure N 2

we know that

m∠C+42°=180° -----> by supplementary angles (form a linear pair)

so

m∠C=180°-42°=138°

Part 3) Which is the measure of ∠B?

see the attached figure N 3

we know that

m∠B and 42° are vertical angles

Remember that the vertical angles are a pair of congruent angles

so

m∠B=42°

Part 4) Find the value of x

see the attached figure N 4

we know that

64° and (3x+1)° are vertical angles

Remember that the vertical angles are a pair of congruent angles

so

64°=(3x+1)°

Solve for x

3x=64-1

3x=63

x=21

Part 5) Find the measure for ∠MQX

see the attached figure N 5

we know that

(3a+39)° and (5a+29)° are vertical angles

Remember that the vertical angles are a pair of congruent angles

so

(3a+39)°=(5a+29)°

Solve for a

5a-3a=39-29

2a=10

a=5

Find the measure of ∠MQX

m∠MQX=(3a+39)°

substitute the value of a

m∠MQX=3(5)+39=54°