Chapter 5: Q11 (page 193)

Two congruent angles of an isosceles trapezoid have measures $3 x + 10$ and $5 x - 10$ . Find the value of x and then give the measures of all angles of the trapezoid.

Short Answer

Expert verified

The value of x is 10 and the measure of other angles is $40, 40, 140$ and $140$ .

Step by step solution

Step 1. Draw and label the diagram.

The figure shows, isosceles trapezoid. Let the measure of angle B be $3 x + 10$ .

Step 2. Apply the property of isosceles trapezoid.

The base angles of an isosceles trapezoid are congruent.

Consider an isosceles trapezoid ABCD such that,

$\begin{array}{l} ∠ A ≅ ∠ D; \\ ∠ B ≅ ∠ C \end{array}$

Therefore $m ∠ B = m ∠ C$

Step 3. Description of step.

Substitute $3 x + 10$ for $m ∠ B$ and $5 x - 10$ for $m ∠ C$ into $m ∠ B = m ∠ C$ .

$\begin{matrix} 3 x + 10 = 5 x - 10 \\ 2 x = 20 \\ x = 10 \end{matrix}$

Step 4. Description of step.

Substitute 10 for x into $m ∠ B = 3 x + 10$

$\begin{matrix} m ∠ B = 3 (10) + 10 \\ = 30 + 10 \\ = 40 \end{matrix}$

Therefore, $m ∠ B = m ∠ C = 40$

Step 5. Description of step.

The sum of the same side interior angles is 180. Therefore,

$\begin{matrix} m ∠ A + m ∠ B = 180 \\ m ∠ A + 40 = 180 \\ m ∠ A = 180 - 40 \\ = 140 \end{matrix}$

Step 6. Description of step.

Substitute 140 for $m ∠ A$ into $m ∠ A = m ∠ D$ to find the value of $m ∠ D$ .

$m ∠ D = 140$

Therefore, the value of x is 10 and the measure of other angles is $40, 40, 140$ and $140$ .

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Two congruent angles of an isosceles trapezoid have measures $3 x + 10$ and $5 x - 10$ . Find the value of x and then give the measures of all angles of the trapezoid.

Short Answer

Step by step solution

Step 1. Draw and label the diagram.

Step 2. Apply the property of isosceles trapezoid.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

Step 6. Description of step.

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Two congruent angles of an isosceles trapezoid have measures 3x+10and 5x-10. Find the value of x and then give the measures of all angles of the trapezoid.

Short Answer

Step by step solution

Step 1. Draw and label the diagram.

Step 2. Apply the property of isosceles trapezoid.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

Step 6. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Logic and Functions

Pure Maths

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Two congruent angles of an isosceles trapezoid have measures $3 x + 10$ and $5 x - 10$ . Find the value of x and then give the measures of all angles of the trapezoid.