Let's recall that the diagonals in a rectangle are congruent and bisect each other.
m∠APB=112^(∘)
Practice makes perfect
Let's begin with recalling that the diagonals in a rectangle are congruent and bisect each other. This means that DP=AP, and triangle DPA is an isosceles triangle. Therefore, m∠DAP=m∠ADP= 56^(∘).
As we know, in a rectangle all angles are right angles. Therefore, the sum of m∠DAP and m∠PAB is equal to 90^(∘).
56^(∘)+m∠PAB=90^(∘)
⇓
m∠PAB= 34^(∘)
Again let's notice that, since diagonals in a rectangle are congruent and bisect each other, triangle APB is an isosceles triangle. This means that m∠ABP=m∠PAB= 34^(∘).
Now, as we are asked to find m∠APB we can use the Triangle Sum Theorem, which tells us that the sum of the measures of all angles in a triangle is always equal to 180^(∘). Let's substitute the measures of ∠PAB and ∠ABP.
