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Q.9

Expert-verifiedFound in: Page 539

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 $x=15\xb0$ and the triangle is **a Scalene triangle**.

One angle of the triangle is $45\xb0$.

Second angle is given as $4x\xb0$.

Third angle is given as $5x\xb0$.

Sum of all angles of a triangle is**$180\xb0$.**

The sum of all the angles of a triangle is$180\xb0$.

This gives us,

$4x{}^{\circ}+5x{}^{\circ}+45{}^{\circ}=180\xb0$

Add both *x* together.

$9x+45{}^{\circ}=180\xb0$

Subtract 45 from both the sides.

$9x+45{}^{\circ}-45{}^{\circ}=180{}^{\circ}-45\xb0$

This gives us,

$9x=135\xb0$

Now, divide both sides by 9.

$\frac{9x\xb0}{9}=\frac{135\xb0}{9}$

This will give us the value of *x*.

$x=15\xb0$

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

To find the value of the angle, multiply it with$15\xb0$.

The angle of second side is 4*x*.

Multiply 4 with 15.

$4x=4\times 15\xb0$

Which gives us the value as$60\xb0$.

The angle of the third side is 5*x*.

And the value is,

$5x=5\times 15\xb0$

Which gives us the value as $75\xb0$.

The value of *x* is $x=15\xb0$.

One angle is $45\xb0$, Second angle is $60\xb0$and the third angle is$75\xb0$.

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

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