Question

One of the angles a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 4:5 find the angle of the triangle​

Answer 1

Given:-

• One of the angles in a triangle is equal to sum of other two angles.
• Ratio of other two angles is 4 : 5

__________________________________

To Find:-

• The angles of the triangle.

__________________________________

Solution:-

Let the ratio of other two angles be 4x and 5x,

$\dashrightarrow \: \: \sf \: 4x + 5x = 9x$

Knowledge required -

• Sum of all angles in a triangle = 180°

So,

$\dashrightarrow \: \: \sf \: 4x + 5x + 9x = 180 \degree$

$\dashrightarrow \: \: \sf \: 18x = 180 \degree$

$\dashrightarrow \: \: \sf \: x = \dfrac{180 \degree}{18}$

$\dashrightarrow \: \: \underline{ \rm{ \purple{ \:x = 10 }}} \:$

Therefore,

The angles in a triangle are :

$\implies \: \tt \: 4x = 4 \times 10 \\ \implies \bf \: 40 \degree$

$\implies \: \tt \: 5x = 5 \times 10 \\ \implies \bf \: 50 \degree$

$\implies \: \tt \: 9x = 9 \times 10 \\ \implies \bf \: 90 \degree$

$\therefore \tt{ \orange{ \: angles \: are \: 40\degree, \: 50 \degree, \: 90 \degree}}$

Answer 2

Step-by-step explanation:

given :

• One of the angles a triangle is equal to the sum of the other two angles. If the ratio of the other two angles is 4:5 find the angle of the triangle

to find :

• find the angle of the triangle

solution :

• The other 2 angles are 4x and 5x for some value of x.

• If the third angle is y then 4x + 5x + y = 180

• And either y = 4x + 5x or 5x = 4x + y.

• If y = 4x + 5x, then x = 10 and the angles are 40 and 50 and 90.

• If 5x = 4x + y, then x = y and x = 18 and the angles are 18 and 72 and 90.