SOLUTION:
Triangle ABD is an Isosceles triangle
1. m < 5 = 30 degrees (base angles of an Isosceles triangle are the same)
2. To find m < 1:
m < 1 + 30 + 30 = 180 ( sum of interior angles in a triangle)
m < 1 = 180 - 60 = 120
m < 1 = 120 degrees.
3. To find m < 2:
< 1 + < 2 = 180 (sum of angles on a straight line)
120 + m < 2 = 180
m < 2 = 180 - 120 = 60
m < 2 = 60 degrees.
4. To find m < 4:
< 4 + < 5 = 90 (angle subtended by semi-circle is 90 degrees at the circumference).
< 4 + 30 = 90 ( m < 5 is 30 from step 1 of the solution)
< 4 = 90 - 30 = 60
m < 4 = 60 degrees.
4. To find m < 3:
< 2 + < 3 + < 4 = 180 ( sum of interior angles in a triangle)
60 + < 3 + 60 = 180
< 3 = 180 - 120
< 3 = 60
m < 3 = 60 degrees.
CONCLUSION:
m < 1 = 120 degrees.
m < 2 = 60 degrees.
m < 3 = 60 degrees.
m < 4 = 60 degrees.
m < 5 = 30 degrees.