Question

1. One of the exterior angles of a triangle is 112 and the corresponding interior opposite angles are
the ratio 3:4. Find the angles of the triangle.​

Answer 1

Answer:

Your Answer is-

Step-by-step explanation:

Let a ∆ABC

Let the exterior angle C = 112 °

Now interior angle C= 68°

Sum of three angles of ∆ =180°_________(i)

Now , angle A: angle B= 3:4

So let angle A=3x

angle B= 4x

Now using (i)

3x + 4x + 68°= 180°

7x+ 68°= 180°

7x= 112°

x= 16

Now angles are A= 48°

B=64°

C=68°~

Answer 2

Your answer Is 68°, 48° 64°.

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Given:-

• One of the exterior angle is 112°.

• And the corresponding opposite interior angles are in 3:4.

To Find:-

• The anglesof a triangle.

Concepts Used:-

Linear Pair:- The sum of angles made a straight angle is always equal to 180°.

Angle Sum Property:- Sum of all interior angles of a traingle are always equal to 180°.

Now,

Let the give triangle be ABC and exterior angle be PCA.

So <CAB:<BAC = 3:4. [Given]

Therefore let these angles be 3x and 4x respectively.

Also,

↦ <ACB + <PCA = 180°.

[By Linear pair]

↦ <ACB + 112° = 180°.

↦ <ACB = 180° - 112°.

↦ <ACB = 68°.

And,

↦ <ACB + <CAB + <BAC = 180°.

↦ 68° + 3x + 4x = 180°.

↦ 3x + 4x = 180° - 68°.

↦ 7x = 112°.

↦ x = 112°/7.

↦ x = 16°.

Therefore,

↦ 3x = 3 × 16° = 48°.

↦ 4x = 4 × 16° = 64°.

So the angles are 68°, 48°, 64°.