Question

Measures of a two angles of a triangle are equal and thrid angle is thric the measure of one of the equal angles.Find the measure of the three angles?​

Answer 1

• Angles of triangle are 36°, 36° and 108°.

Step-by-step explanation:

To find:-

• Measure of all three angles of triangle.

Solution:-

Given that,

Measures of a two angles of a triangle are equal and thrid angle is thrice the measure of one of the equal angles.

Let, Two equal angles of triangle be x and x.

And, Third angle of triangle be 3x [Given, Third angle is thrice the measure of any one equal angles]

We know,

Sum of all interior angles of triangle is 180°. This statement is known as 'Angle sum property of triangle'.

So,

➝ x + x + 3x = 180°

➝ 5x = 180°

➝ x = 180°/5

➝ x = 36°

Verification:-

➝ x + x + 3x = 180°

➝ 36° + 36° + 3×36° = 180°

➝ 36° + 36° + 108° = 180°

➝ 180° = 180°

Hence, Verified.

We have taken, Two equal angles be x and x. Thus, Two equal angles of triangle are 36° and 36°.

We have also taken, Third angle be 3x = 3×36 = 108°. So, Third angle of triangle is 108°.

Answer 2

Step-by-step explanation:

Given :

• Measures of a two angles of a triangle are equal .

• thrid angle is thric the measure of one of the equal angles.

To Find :

• Find the measure of the three angles?

Solution :

According to the Question :

Measures of a two angles of a triangle are equal then,

• The fisrt and second number is x

Thrid angle is thric the measure of one of the equal angles then,

• Third number is 3x

We know that :

• Total measures of all the angles of a triangle is 180°.

Then ,

$: \implies \sf \: \: \: \: \: \: \: x \: + \: x + 3x \: = 180 \\ \\ \\ : \implies \sf \: \: \: \: \: \: \:5x = 180 \\ \\ \\ : \implies \sf \: \: \: \: \: \: \:x = \cancel{\frac{180}{5} } \\ \\ \\ : \implies \sf \: \: \: \: \: \: \: x = 36$

Hence ,

• First number = x = 36°

• Second number. = x = 36°

• Third numer = 3x = 3 × 36 = 108°

more to know :

Three Types of Angles : -

• Using a Protractor. The best way to measure an angle is to use a protractor.

• Angles in Triangles. Triangles received their name from the three angles that they possess.

• Angles in Quadrilaterals. Squares and rectangles have four right angles. .