Examining the diagram, we see that the sum of ∠ a and 37^(∘) makes a vertical angle to the 63^(∘) angle. By the Vertical Angles Theorem, we know that these angles are congruent.
Since the two angles are congruent, we can equate their measures and solve the resulting equation for m∠ a.
37^(∘)+m∠ a=63^(∘) ⇔ m∠ a=26^(∘)
When we know the measure of ∠ b, we have enough information to find ∠ d. For this purpose, we will isolate a second triangle we can see in the diagram.
Notice that ∠ d is exterior angle to the triangle we see in the diagram. By the Exterior Angles Theorem, we know that ∠ d equals the sum of the triangles non-adjacent angles.
m∠ d=65^(∘)+52^(∘) ⇔ m∠ d=117^(∘)
