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Step-by-step explanation:

First we know triangle WXY is an equilateral which means all its angles are 60 degrees.

Next we know triangle WZY is an isosceles so it has 2 angles that are equal to each other.  

Since angle Z is an obtuse angle. We can calculate the other angles which we will assume are equal because 138+138 is greater than 180 degrees.

180-138 = 42                

42/2 = 21              <-- divide by 2 because we know we're looking for 2 angles

For the angles of WXY.

60-21 = 39

Therefore

Angle I = 60

Angle 2 = 39

Angle 3 = 21

Angle 4 = 39

Angle 5 = 21

m<1=60°

m<2=39°

m<3=21°

m<4=39°

m<5=21°

Step-by-step explanation:

since triangle WZY is isosceles, this means that the measure of angle 3 is the same as measure of angle 5.

to find out what they equal:

180-138=42.

then divide by 2 since angle 3 and angle 5 are congruent.

42/2=21°.

m<3 =21° and m<5 =21°

triangle WXY is equilateral, and an equilateral triangle has 60° angles.

so, m<1=60°.

however, to find m<2 and m<4 we would have to subtract 60° from 21°:

60°-21°=39°.

so, m<2 =39°, and m<4=39°