Question

One angle of a triangle is equal to the sum of the other two angles. The smaller angles are in the ratio 2 : 3. What are the angles of the triangle ?​

Answer 1

Step-by-step explanation:

let the angle be be x

then:

2x, 3x

the bigger angle is

2x+3x= 5x

So now we have three angles . And sum of 3 angles of a triangle is 180 degree

then :

2x+3x+5x=180

10x=180

x=18

2×18=36

3×18=54

5×18=90

Answer 2

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Given

• Ratio of smaller angles = 2 : 3

• Third Angle equal to sum of other two angles

To Find

• All angles of triangle

Solution

Let the small angles be 2x and 3x.

Then, the third angle will be = 2x + 3x

= 5x

According to question,

➨2x + 3x + 5x = 180° [ Angle Sum Property ]

➨ 10x = 180°

➨ x = 180°/10

➨x = 18°

Therefore, angles are :-

2x ➨ 2 × 18

= 36°

3x ➨ 3 × 18

= 54°

5x ➨ 5 × 18

= 90°

Angles of the triangle are 36°, 54° and 90°