Question

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

Answer 1

Answer:

Part 1) Option D. must be an acute angle

Part 2) m∠A=70°

Step-by-step 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°