Question

Ona angle of a traingle is 27degree. If the ratio of remaining two angles is 8:9,find all the angle of the traingle in grade​

Answer 1

Answer:

27°, 72° and 81°are all the angles of the triangle.

Step-by-step explanation:

One angle of the triangle = 27°

Let the highest common factor between the remaining two angle is "x"

The second angle of the triangle = 8x

The third angle of the triangle = 9x

By angle sum property, sum of all angles of a triangle is 180°. Here 27°, 8x and 9x are the angles.

⇏ 27° + 8x + 9x = 180°

⇏ 8x + 9x = 180° - 27°

⇏ 8x + 9x = 153°

⇏ 17x = 153°

⇏ x = 153°/17

⇏ x = 9°

The second angle of the triangle = 8x = 8(9°) = 72°

The third angle of the triangle = 9x = 9(9°) = 81°

Double check:

All the angles of the the triangle must sum up to 180°

⇏ 1st angle + 2nd angle + 3rd angle = 180°

⇏ 27° + 72° + 81° = 180°

⇏ 180° = 180°

LHS = RHS, hence the Answer is correct

Answer 2

Given :-

• Shape = Triangle
• One angle of a traingle is 27°
• The ratio of remaining two angles is 8:9

To Find :-

• All Angles of the Triangle.

Solution :-

In this Question, it is given that First angle of the Triangle is of 27° and the remaining two angles are in the ratio of 8:9 and we have to find all the angles of the Triangle. For finding the other two angles we will apply Angles Sum Property of Triangle this means 1st angle + 2nd angle + 3rd angle = 180°.

It was given that the other two angles of the Triangle are in ratio 8:9 Therefore :

⟹ Let the First angle be 27°

⟹ Let the Second angle be 8x

⟹ Let the Third angle be 9x

According to the Question :

⟶ 1st angle + 2nd angle + 3rd angle = 180

⟶ 27 + 8x + 9x = 180

⟶ 27 + 17x = 180

⟶ 17x = 180 - 27

⟶ 17x = 153

⟶ x = 153 ÷ 17

⟶ x = 9

Therefore :-

➥ First angle = 27°

➥ Second angle = 8x = 8 × 9 = 72°

➥ Third angle = 9x = 9 × 9 = 81°

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