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Q.9

Expert-verified
Found in: Page 539

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# 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.

See the step by step solution

## Step 1. Given Information.

One angle of the triangle is $45°$.

Second angle is given as $4x°$.

Third angle is given as $5x°$.

## 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,

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

$9x+45{}^{\circ }=180°$

Subtract 45 from both the sides.

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

This gives us,

$9x=135°$

Now, divide both sides by 9.

$\frac{9x°}{9}=\frac{135°}{9}$

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.

$4x=4×15°$

Which gives us the value as$60°$.

The angle of the third side is 5x.

And the value is,

$5x=5×15°$

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.