Question

In triangle ABC, if an exterior angle drawn at vertex C

measures 45, then angle B
A.must be an obtuse angle
B. must be a right angle
C.may be either an obtuse angle or an acute angle
D.must be an acute angle
Question 2
In triangle ABC, the measure of an exterior angle at B is 5 more
than twice the measure of ZC. If m2C = 65, what is
MZA?
A.45
B.70
C.110
D.135

Answer 1

Part 1) Option D. must be an acute angle

Part 2) m∠A=70°

Explanation:

Part 1) In triangle ABC, if an exterior angle drawn at vertex C measures 45, then angle B...

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

so

The measure of an exterior angle at C is equal to the sum of the interior angles at A and B

we have that

45°=m∠A+m∠B

therefore

m∠B < 90°

Angle B must be an acute angle

Part 2)

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles

so

The measure of an exterior angle at B is equal to the sum of the interior angles at A and C

m∠A+m∠C=2m∠C+5

m∠C=m∠A-5 ----> equation A

m∠C=65° ----> equation B

substitute equation B in equation A

65°=m∠A-5

m∠A=(65+5)°=70°