From previous exercises, we know that the measure of ∠3 is 50^(∘) and the measure of ∠5 is 40^(∘).
According to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. We see that ∠7 is exterior angle to the 90^(∘) angle of the smaller triangle. Therefore, we can equate it's measure with the sum of the two nonadjacent angles, 50^(∘) and 40^(∘).
m∠7=50^(∘)+40^(∘).
By simplifying the equation, we can find the measure of ∠7.
