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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 5: Q20 (page 170)

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Short Answer

Expert verified

The value of x and y is 7 and 18 respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

Diagonals of a parallelogram bisect each other, that is, two segments of each diagonal are equal to one another.

In a given figure, by the property of a parallelogram,

$\begin{matrix} 3 x + 4 = 25; \\ 2 y - 8 = 28 \end{matrix}$

02

Step 2. Description of step.

Subtract 4 from both sides of $3 x + 4 = 25$ .

$\begin{matrix} 3 x + 4 - 4 = 25 - 4 \\ 3 x = 21 \end{matrix}$

03

Step 3. Description of step.

Divide each side of $3 x = 21$ by 3 to obtain the value of x.

$\begin{matrix} \frac{3 x}{3} = \frac{21}{3} \\ x = 7 \end{matrix}$

04

Step 4. Description of step.

Add 8 on both sides of $2 y - 8 = 28$ .

$\begin{matrix} 2 y - 8 + 8 = 28 + 8 \\ 2 y = 36 \end{matrix}$

05

Step 5. Description of step.

Divide each side of $2 y = 36$ by 2 to obtain the value of y.

$\begin{matrix} \frac{2 y}{2} = \frac{36}{2} \\ y = 18 \end{matrix}$

Therefore, the value of x and y is 7 and 18 respectively.

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Most popular questions from this chapter

M, N and T are the midpoints of the sides of $Δ XYZ$ .

If $XZ = 10$ , then $MN = \underline{?}$

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Each figure in Exercises 19-24 is a parallelogram with its diagonals drawn. Find the values of x and y.

Draw two segments that are both parallel and congruent. Connect their endpoints to form a quadrilateral. What appears to be true of the quadrilateral?

$▱ DECK$ is a parallelogram. Complete.

If $m ∠ 1 = 3 x, m ∠ 2 = 4 x$ and $m ∠ 3 = x^{2} - 70$ then $x = ?$ and $m ∠ CED = ?$ (numerical answers).

See all solutions

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