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Q.4

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* is $x=65\xb0$, and the triangle is a **scalene right-angled** **triangle**.

One angle of the triangle is $25\xb0$.

Second angle is given as $x\xb0$.

Third angle is given as $\left(x+25\right)\xb0$.

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,

$x+\left(x+25\right){}^{\circ}+25{}^{\circ}=180\xb0$

Add both *x* and both numbers together.

$2x+50{}^{\circ}=180\xb0$

Subtract 50 from both the sides.

$2x+50{}^{\circ}-50{}^{\circ}=180{}^{\circ}-50\xb0$

This gives us,

$2x=130\xb0$

Now, divide both sides by 2.

$\frac{2x\xb0}{2}=\frac{130\xb0}{2}$

This will give us the value of *x*.

$x=65\xb0$

Second side of the angle of the triangle is given as $x\xb0$ which is$65\xb0$.

Third side of the angle of the triangle is given as $\left(x+25\right)\xb0$.

Now add $65\xb0$ to it.

This gives us the value as,

$65{}^{\circ}+25{}^{\circ}=90\xb0$

The value of *x* is $x=65\xb0$.

Since one angle of the triangle is $90\xb0$ and the other two angles are $25\xb0$ and $65\xb0$ respectively.

Hence, it is a scalene right-angled triangle.

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