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snow_tiger [21]
3 years ago
14

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

Mathematics
1 answer:
Lorico [155]3 years ago
3 0

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°

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