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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 26 Page 533

If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

x = 4, y = 8

Practice makes perfect

We want to find the values of x and y so that a quadrilateral is a parallelogram.

Let's find the value of each variable one at a time.

Value of x

The angles that measure 12x + 72 and 25x + 20 are opposite angles. Recall the Theorem 6.10, which tells us that if both pairs of opposite angles in quadrilateral are congruent, then the quadrilateral is a parallelogram. Therefore, the measures of these angles must be equal. 12x + 72= 25x + 20 Let's solve this equation to find a value of x.

12x + 72 = 25x + 20

LHS-72=RHS-72

12x = 25x - 52

LHS-25x=RHS-25x

- 13x = - 52

.LHS /(- 13).=.RHS /(- 13).

x = 4

Value of y

Similarly, the angles that measure 9y - 12 and 3y + 36 are also opposite angles. Recall the same theorem once again. The measures of these angles must be equal. 9y - 12= 3y + 36 Let's solve the equation to find a value of y.

9y - 12 = 3y + 36

LHS-3y=RHS-3y

6y - 12 = 36

LHS+12=RHS+12

6y = 48

.LHS /6.=.RHS /6.

y = 8

Subchapter links

1 Angles of Polygons p.532

2 Parallelograms p.532

3 Tests for Parallelograms p.533

4 Rectangles p.533

5 Rhombi and Squares p.534

6 Trapezoids and Kites p.534