Exercise 26 Page 509

Let's analyze the given quadrilateral so that we can find the measure of ∠ 1.

By the definition of a rectangle, we know that ABCD has four right angles. Therefore, the measure of m ∠ BAD is 90. m ∠ BAD= 90 With the Angle Addition Postulate we can express m ∠ BAD as a sum of m ∠ 1 and m ∠ 2. m ∠ 1 + m ∠ 2 = m ∠ BAD ⇕ m ∠ 1 + m ∠ 2 = 90 We are given that m ∠ 2= 40. We will substitute it into our equation. m ∠ 1 + 40 = 90 Let's solve it!

m ∠ 1 + 40 = 90

SubEqn

LHS-40=RHS-40

m ∠ 1 = 50