Question

One angle of a triangle is 55 and the ratio of the other two angles is 8 : 17. Find the measures of the remaining angles.​

Answer 1

Answer:

The measures of other two angles are $40$°, $85$°.

Step-by-step explanation:

Given one angle of a triangle as $55\degree$°.

The other angles are in the ratio $8:17$.

We know, the sum of angles of a triangle is $180$°.

Let the other two angles are $8x,17x$.

⇒$55+8x+17x=180$

$25x=180-55$

$25x=125\\x=5$

$8x=40$

$17x=85$

The other two angles are $40$°, $85$°.

Answer 2

Given,

One angle of a triangle is $55^{0}$ and the ratio of the other two angles is $8:17$.

We have to find the measures of the remaining angles

We know that,

The sum of the angles of a triangles is $180^{0}$.

Let other two angles be $8x,17x$

According to the question,

One angle of a triangle is $55^{0}$

$8x+17x+55=180$

$25x=180-55$

$25x=125x$

$x= \frac{125}{25}$

$x=$$5$

Now, substitute $x=$$5$ in $8x$ and $17x$

$8x=8\times 5$

$=40$

$17x=17\times 5$

$=85$

Therefore, the remaining angles are $40^{0}$ and $85^{0}$.