Find M∠1 If M∠8 = 63°​

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