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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 18 Page 504

Recall the theorem which states that if a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

d=42, f=14

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

Value of d

Notice that the angles measuring 56^(∘) and (3d-2)^(∘) are consecutive angles. Recall the theorem that says:

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

Therefore, the measures of our consecutive angles add up to 180^(∘). 56+ (3d-2)=180 Let's solve it!

56+(3d-2)=180

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Solve for d

Remove parentheses

56+3d-2=180

Subtract term

54+3d=180

LHS-54=RHS-54

3d = 126

LHS+2=RHS+2

3d = 126

.LHS /3.=.RHS /3.

d=42

Value of f

Notice that the sides with the lengths measuring 3f-6 and 2f+8 are opposite sides in our parallelogram. Recall the following theorem.

If a quadrilateral is a parallelogram, then its opposite sides are congruent.

Therefore, the lengths of the opposite sides are equal. 3f-6=2f+8 Now, let's solve for f.

3f-6=2f+8

LHS+6=RHS+6

3f = 2f + 14

LHS-2f=RHS-2f

f = 14