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

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°

answer: d. $20

step-by-step explanation:

just took the test

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12