# PROPERTIES OF TRIANGLE WORKSHEET

Problem 1 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Problem 2 :

In a triangle, if the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

Problem 3 :

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

Problem 4 :

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

Problem 1 :

If the angles of a triangle are in the ratio 2 : 7 : 11, then find the angles.

Solution :

From the ratio 2 : 7 : 11,

the three angles are 2x, 7x, 11x

In any triangle, sum of the angles = 180°

So, 2x + 7x + 11x  =  180°

20x  =  180 -------> x  =  9

Then, the first angle  =  2x  =  2(9)  = 18°

The second angle  =  7x  =  7(9)  =  63°

The third angle  =  11x  =  11(9)  99°

So, the angles of the triangle are (18°, 63°, 99°)

Problem 2 :

In a triangle, if the second angle is 10% more than the first angle and the third angle is 20% less than the first angle, then find the three angles of the triangle.

Solution :

Let 'x' be the first angle.

The second angle  =  120 % of x  =  1.2x

The third angle  =  80% of x  =  0.8x

We know that,

the sum of the three angles of a triangle  =  180°

x + 1.2x + 0.8x  =  180°

3x  =  180°

x  =  60°

The first angle  =  60°

The second angle  =  1.2(60)  =  72°

The third angle  =  0.8(60)  =  48°

So, the three angles of a triangle are 60°, 72° and 48°.

Problem 3 :

If 3 consecutive positive integers be the angles of a triangle, then find the three angles of the triangle.

Solution :

Let 'x' be the first angle.

The second angle  =  x + 1

The third angle  =  x + 1 + 1  =  x + 2

We know that,

the sum of the three angles of a triangle  =  180°

x + x + 1 + x + 2  =  180°

3x + 3  =  180°

3x  =  177°

x  =  59°

The first angle  =  59°

The second angle  =  59 + 1  =  60°

The third angle  =  60 + 1  =  61°

So, the three angles of a triangle are 59°, 60° and 61°.

Problem 4 :

In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of the triangle.

Solution :

Let "x" be the first angle.

The second angle  =  2x

The third angle  =  3x

We know that,

the sum of the three angles of a triangle  =  180°

x + 2x + 3x  =  180°

6x  =  180°

x  =  30°

The first angle  =  30°

The second angle  =  2(30°)  =  60°

The third angle  =  3(30°)  =  90°

So, the three angles of a triangle are 30°, 60° and 90°.

Apart from the problems given above, if you need more problems on triangle properties, please click the following links.

Worksheet on Properties of Triangle

Worksheet on Properties of Triangle 1

Worksheet on Properties of Triangle 3

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