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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Parallelograms

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Exercise 16 Page 490

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

x=79, y=101

Practice makes perfect

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

Value of x

Notice that the angles measuring 101^(∘) and x^(∘) are consecutive angles. Recall the following theorem.

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

Therefore, the measures of these consecutive angles add up to 180. x+ 101=180 Let's solve it!

x+101=180

LHS-101=RHS-101

x=79

Value of y

Notice that the angles that measure 101^(∘) and y^(∘) are opposite angles. Recall the theorem opposite angles of a parallelogram are congruent. Therefore, the measures of these angles are equal. y= 101

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Exercises p.489-493