Question

one of the angles of triangle is equal to the sum of other two angles if the ratio of other two angles is 4:5 find all angles of a triangle​

Answer 1

Answer:

Let a, b, c be the angles of the triangle.

As you know, a+b+c=180° (1) in a triangle.

a=b+c (2)

b/c = 4/5, so 5b=4c or c=5/4 b (3)

From (2) & (3): a=b + 5/4 b = 9/4 b or a = 9/4 b (4)

From (1)&(3)&(4) one gets:

9/4 b + b + 5/4 b = 180°

It means that 18/4 b = 180° so,

b = 40°. Then c = 5/4 • 40° and

c = 50° .

a = b + c = 40° + 50° = 90°

Your angles are 90° , 50° and 40°.

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Carl Bryan, B.S. Mathematics, Carnegie Mellon University (1972)

Answered June 26, 2018 · Author has 4.2K answers and 1.4M answer views

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.

Answer 2

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❥ɢɨʋɛռ

• ratio of other two angles is 4:5

• one of the angles of triangle is equal to the sum of other two angles

❥ȶօ ʄɨռɖ

• All angles of triangle

❥Sօʟʊȶɨօռ

Let the angles be 4x and 5x

then, third angle will be 4x + 5x = 9x

According to question,

${\implies}4x + 5x + 9x = 180°$

${\implies}18x = 180°$

${\implies}x = 180 \div 18$

${\implies}x = 10$

Therefore, angles are

➨ 4x = 4 × 10 = 40°

➨5x = 5 × 10 = 50°

➨9x = 9 × 10 = 90°

hope it helps you.....✌