Chapter 5: Q7 (page 169)

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

Short Answer

Expert verified

The values of a, b, x and y are $5, 3, 120 °$ and $22 °$ respectively.

Step by step solution

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

Step 2. Description of step.

In the given figure, $\bar{P S} ≅ \bar{Q R}$ implies that $a = 5$ and $\bar{P Q} ≅ \bar{S R}$ implies that $b = 3$ .

Step 3. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

Step 4. Description of step.

From the given figure, it can be observed that $∠ x ≅ ∠ P S R$ implies that

$\begin{matrix} x = m ∠ P S R \\ = 120 ° \end{matrix}$

Step 5. Description of step.

Consider $Δ P Q R$ ,

The sum of measures of all angles of a triangle is 180. Therefore,

$\begin{matrix} m ∠ Q P R + m ∠ P Q R + m ∠ Q R P = 180 \\ 38 + 120 + m ∠ Q R P = 180 \\ m ∠ Q R P = 180 - 158 \\ = 22 ° \end{matrix}$

Step 6. Description of step.

Both pairs of opposite sides of a parallelogram are parallel, that is, $\bar{P S} | | \bar{Q R}$ and $\bar{S Q}$ is a transversal then angle made by a transversal with respect to two lines are equal.

$∠ S P R ≅ ∠ Q R P$

Therefore,

$\begin{matrix} m ∠ S P R = m ∠ Q R P = 22 ° \\ x = 22 ° \end{matrix}$

Therefore, the values of a, b, x and y are $5, 3, 120 °$ and $22 °$ respectively.

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In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Apply property of parallelogram.

Step 4. Description of step.

Step 5. Description of step.

Step 6. Description of step.

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