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 $x = 15 °$ and the triangle is a Scalene triangle.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

One angle of the triangle is $45 °$ .

Second angle is given as $4 x °$ .

Third angle is given as $5 x °$ .

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,

$4 x {}^{\circ}+ 5 x {}^{\circ}+ 45 {}^{\circ}= 180 °$

Add both x together.

$9 x + 45 {}^{\circ}= 180 °$

Subtract 45 from both the sides.

$9 x + 45 {}^{\circ}- 45 {}^{\circ}= 180 {}^{\circ}- 45 °$

This gives us,

$9 x = 135 °$

Now, divide both sides by 9.

$\frac{9 x °}{9} = \frac{135 °}{9}$

This will give us the value of x.

$x = 15 °$

Since, the other two angles of the triangle are 4x and 5x.

To find the value of the angle, multiply it with $15 °$ .

The angle of second side is 4x.

Multiply 4 with 15.

$4 x = 4 \times 15 °$

Which gives us the value as $60 °$ .

The angle of the third side is 5x.

And the value is,

$5 x = 5 \times 15 °$

Which gives us the value as $75 °$ .

Step 4. Conclusion.

The value of x is $x = 15 °$ .

One angle is $45 °$ , Second angle is $60 °$ and the third angle is $75 °$ .

All the three angles of the triangle are different. Hence, it is a scalene right-angled triangle.

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Pre-algebra

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Short Answer

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

Step by Step Solution

Step 1. Given Information.

Step 2. Formula.

Step 3. Calculation.

Step 4. Conclusion.

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