Question

Two angles of a triangles are in the ratio 4:5. If the sum of these angles is equal to the third angle,find the angles of the triangles.​

Answer 1

Given:

• Two angles of triangle are in ratio 4:5.

• sum of these angles equal to third angle.

To find:

• Angles of the triangle :

Solution:

Let the angles of the traingle be A , B and C ,

A/Q

$\star \: \angle \: A = 4x \\ \\ \star \angle \: B = 5x \\ \\ \star \angle \: C = 4x + 5x = 9x$

As we know that :

sum of all angles of traingle is 180°

$\star \: \angle \: A + \angle \:B + \angle \: C = 180 \degree \\ \\ \implies \: 4x + 5x + 9x = 180 \degree \\ \\ \implies18x = 180 \degree \\ \\ \implies \: x = 10 \degree$

Now put the value of x and we get all the angles of triangle.

$\star \angle \: A = 4x = 40 \degree \\ \\ \star \angle B = 5x = 50 \degree \\ \\ \star \angle C = 9x = 90 \degree$

Answer 2

Answer:

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Let the two angles of the triangle be 4x and 5x.

Then, as per the question, we know

third angle =4x+5x=9x

We know that sum of all the angles of a triangle is 180°

Therefore

$4x + 5x + 9x = 180 °$

$= > 18x = 180°$

$= > x = 10°$

....[On dividing both sides by 18]

So, first angle = 4x°

=4×10°

=40°

second angle =5x°

= 5×10°

= 50°

third angle = 9x°

=9×10°

=90°