Question

M<2, M<3 (find the measure of each angle)

Answer 1

One of the triangles (that on the left, top) has 2 equal sides, and thus is isosceles.  The angle immediately adjacent to and to the right of 110 degrees is 180-110 degrees, or 70 degrees, which means that angle 1 is also 70 degrees.  The remaining angle is 180 degrees less 2(70 degrees), or 40 degrees; thus, angle 2, immediately adjacent to and to the right of this 40 degree angle, is 180-40, or 140 degrees.  The triangle to the right and below the horiz. line has angle 40 degrees (using the principle of vertical angles); thus, angle 3 is 180-(40+90) degrees, or 50 degrees.

Answer 2

1st triangle (left)
This is an isosceles triangle.
1) The angle near 110⁰ is (180-110)= 70⁰.
2)m ∠ 1 = 70⁰, because this triangle is isosceles.
3) (180 - m∠2)

Sum of three angles
70 + 70 + 180 - m∠2 =180
70+ 70 - m∠2 = 0
m∠2 = 140⁰

Second triangle (right)
1) (180 - m∠2)
2) m∠ 3
3) 90⁰

Sum of three angles
180 - m∠2 +m∠3+90 = 180
- 140 +m∠3+90 = 0
m∠3 = 50⁰

Answer:
m ∠ 1 = 70⁰,
m∠2 = 140⁰,
m∠3 = 50⁰.