Question

if the angle of a triangle are in the ratio 1:2:1 , find all the angle of the triangle classify the triangle in two different ways​

Answer 1

Step-by-step explanation:

the triangle is isosceles triangle ️ so measures of triangle are

1x +2x +1x = 180 degree

4x = 180

x= 180/4

x = 45

1x = 45

2x = 45 x 2

= 90

so, the measures of triangle are 45, 90 , 45,

.

. . 45, 90, 45 = 1:2:1

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Answer 2

Given :-

• Ratio of the angles of triangle = 1 : 2 : 1

To find :-

• All the angles of triangle and classify the triangle in two different ways.

Knowledge Required :-

• Formula to calculate sum of interior angles of a polygon.

• Sum of interior angles of a polygon = (2n - 4) × 90°

where,

• n = number of sides of the polygon

Solution :-

Let the angles of triangle be x, 2x and x.

• First angle = x
• Second angle = 2x
• Third angle = x

Triangle has 3 sides, 3 angles.

Number of sides (n) = 3

→ x + 2x + x = (2n - 4) × 90°

→ 4x = ((2 × 3) - 4) × 90°

→ 4x = (6 - 4) × 90°

→ 4x = 2 × 90°

→ 4x = 180°

→ x = 180°/4

→ x = 45°

The value of x = 45°

Substitute the value of x in the angles of triangle.

→ First angle = x = 45°

→ Second angle = 2x = 2 × 45° = 90°

→ Third angle = x = 45°

• Therefore, the three angles of triangle are 45°, 90° and 45°.

The triangle is an Isosceles triangle because two angles are equal to each other and third angle is unequal and also it is a right - angled triangle as one of the angle is 90°.

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Verification :-

Add all the three angles of triangle if their sum is equal to 180°, then the values are right.

→ 45° + 90° + 45°

→ 180°

Sum of angles of triangle = 180°.

Hence, verified