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Q.3

Expert-verified

Pre-algebra

Found in: Page 539

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Find the value of x. Then classify the triangle by its angle measures.

The value of x is $x = 20 °$ and the triangle is an isosceles triangle.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

One angle of the triangle is $80 °$ .

Second angle is given as $4 x °$ .

Third angle is given as $x °$ .

Step 2. Formula.

Sum of all angles of a triangle is $180 °$ .

Step 3. Calculation.

The sum of all the angles of a triangle is $180 °$ .

This gives us,

$4 x {}^{\circ}+ x {}^{\circ}+ 80 {}^{\circ}= 180 °$

Add both x together.

$5 x + 80 {}^{\circ}= 180 °$

Subtract 80 from both the sides.

$5 x + 80 {}^{\circ}- 80 {}^{\circ}= 180 {}^{\circ}- 80 °$

This gives us,

$5 x = 100 °$

Now, divide both sides by 5.

$\frac{5 x}{5} = \frac{120 °}{5}$

This will give us,

$x = 20 °$

Since, the other two angles of the triangle are 4x and x.

To find the value of the angles multiply it with 20.

The angle of second side is 4x.

Multiply it with 4.

$4 x = 4 \times 20 °$

Which gives the value as $80 °$ .

The angle of the third side is x.

And the value of x is $x = 20 °$ .

Which gives us the value as $20 °$ .

Step 4. Conclusion.

The value of x is $x = 20 °$ .

One angle is $80 °$ , Second angle is $80 °$ and the third angle is $20 °$ .

Two sides of the triangle are same and one is different.

Hence, it is an isosceles triangle.

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