Question

The angles of a triangle are in the ratio of 3: 4: 2. Find the measure of
each angle of the triangle.
​

Answer 1

Given

Angles of Triangle are in the ratio 3:4:2

To Find

measures of each angle of triangle

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

let's discusss some properties of triangle:

=>The triangle have 3 sides and 3 vertices.

=>There are three angles in a triangle and they all makes sum of 180°.

Reason: Angle sum property of Triangle

Now,we have given angles in the ratio so,each angle would be 3x,4x & 2x respectively.

Now , applying angle sum property:

=>3x+4x+2x=180°

=>7x+2x=180°

=>9x=180°

=>x=180÷9

=>x=20°

x=20°

Now, finding all angles of triangle:

first angle = 3x=>3×20°=60°

Second angle=>4x=4×20°=80°

Third angle=>2x=>2×20°=40°

check:-

=>60°+80°+40°

=>100°+80°

=180°

Extra information=>

• In an equilateral triangle the measure of each angle is 60°.
• In an Isosceles triangle two angles are equal of two equal sides.
• The sum of two angles is equal to the angle outside this is called 'exterior angle theorem'.

Answer 2

Answer:

Let the angles are 2x, 3x and 4x. According to the angle sum property, the sum of interior angles of a triangle is 180 degree. The value of x is 20. Therefore the angles of triangle are 40, 60 and 80.