Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 35 Page 423

Notice that for a kite the diagonals are perpendicular.

m∠ 1 =90
m∠ 2 =45

Practice makes perfect

Let's find the measures of the numbered angles one at a time.

Measure of ∠ 1

Before we begin, let's name the vertices of our kite. We will call it quadrilateral ABCD. The angle that forms a linear pair with ∠ 1 we will label M.

If a quadrilateral is a kite, then its diagonals are perpendicular. Therefore, ∠ 1 is right and its measure is 90.

Measure of ∠ 2

We have a triangle with the angles ∠ M, ∠ 2, and the angle with measure 65. By the Triangle Angle-Sum Theorem we know that the measures of the angles add to 180. 45+ m∠ M+m∠ 2=180 Since ∠ M is formed by the diagonals it is right and its measure is 90. Let's substitute 90 for m∠ M and solve the equation.
45+ m∠ M+m∠ 2=180
45+ 90+m∠ 2=180
Solve for m∠ 2
135+m∠ 2=180
m∠ 2=45