body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Parallelograms

Continue to next subchapter

Exercise 19 Page 490

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

x=58, y=63.5

Practice makes perfect

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

Value of x

Notice that the angles measuring (x-5)^(∘) and (2x+11)^(∘) are consecutive angles. Recall the following theorem.

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

Therefore, the measures of our consecutive angles add up to 180. (x-5)+ (2x+11)=180 Let's solve it!

(x-5)+(2x+11)=180

Remove parentheses

x-5+2x+11=180

Add and subtract terms

3x+6=180

LHS-6=RHS-6

3x=174

.LHS /3.=.RHS /3.

x=58

Value of y

Notice that the angles that measure 2y^(∘) and (2x+11)^(∘) are opposite angles. Recall the theorem that tells us that if a quadrilateral is a parallelogram then its opposite angles are congruent. Therefore, the measures of these angles are equal. 2y= (2x+11) We can find the value of y by substituting the value of x that we have just found into the equation and solving for y.

2y=(2x+11)

Remove parentheses

2y=2x+11

x= 58

2y=2(58)+11

Multiply

2y=116+11

Add terms

2y=127

.LHS /2.=.RHS /2.

y=63.5

Subchapter links

Exercises p.489-493