find m∠1 if m∠8 = 63°
Answer:
1. If m 2=63, what is m 3?
Since Triangle LMN has two sides that are congruent, it is an Isosceles triangle; it also follows that the base angles are congruent. Given that the measure of one of the base angles, angle 2 = 63, the other base angle which is MNL is also 63. Notice also that angle 3 is half the vertex angle LMN.
The sum of the measures of the angles in a triangle is 180.
63+63+2(Angle3) = 18063+63+2(Angle3)=180
2(Angle 3)=180-126=542(Angle3)=180−126=54
Angle 3= \frac{54}{2} =27^{0} Angle3=
2
54
=27
0
Angle 3 = 27 degrees
7. If m angle 3 = 31, what is m angle LMN?
The measure of LMN is twice the measure of angle 3. So,
Measure of angle LMN = 2(angle 3) = 2(31) = 62 degrees
