Question

How do I solve this question I’ve been stuck on this since last night

Answer 1

Observation one

From the markings on the diagram <1 = 60o The left triangle is at least isosceles. Therefore equal sides produce equal angles opposite them.

Now we have accounted for 2 angles that are equal (each is 60 degrees) and add up to 120 degrees. The third angle (angle 2) is found from this equation.

<1 + 60 + <2 = 180 degrees.  All triangles have 180 degrees.

60 + 60 + <2 = 180

Observation 2

<2 = 60 degrees.

120 + <2 = 180

m<2 = 180 - 120

m<2 = 60 degrees.

Observation 3

m<3 = 120

<2 and <3 are supplementary.

Any 2 angles on the same straight line are supplementary

60 + <3 = 180

<3 = 180 - 60

<3 = 120

Observation 4

m<4 = 40 degrees.

All triangles have 180 degrees. No exceptions.

m<4 + 20 +m<3 = 180

m<4 + 20 + 120 = 180

m<4 + 140 = 180          

m<4 = 180 - 140

m<4 = 40