Consider Kite KlLMN 1)if M 2=63 What Is M 3? 7)if M Angle 3=31…

consider kite KlLMN
1)if m 2=63 what is m 3?
7)if m angle 3=31,what is m angle LMN?

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.

[tex]63+63+2(Angle3) = 180[/tex]

[tex]2(Angle 3)=180-126=54[/tex]

[tex]Angle 3= \frac{54}{2} =27^{0} [/tex]

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