Answer:
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°
Step-by-step 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°
