Answer:
angle NMP = 63°
angle LMP = 74°
Step-by-step explanation:
Let angle NMP be x° . It's given that angle LMP is 11° more than angle NMP. So, angle LMP = x° + 11°
But angle NML = 137°.
So,
angle NMP + angle LMP = 137°
=> x° + x° + 11° = 137°
=> 2x° + 11° = 137°
=> 2x° = 137° - 11°
= 126°
=> x° = 126/2 = 63°
angle NMP = 63°
angle LMP = 63 + 11 = 74°
This is an isosceles triangle. Therefore, at the base we have congruent angles (look at the picture).
We have the equation:
(5x + 13)° + (3x + 7)° = 180°
5x + 13 + 3x + 7 = 180 <em>combine like terms</em>
(5x + 3x) + (13 + 7) = 180
8x + 20 = 180 <em>subtract 20 from both sides</em>
8x = 160 <em>divide both sides by 8</em>
<h3>x = 20</h3>