Question

Angles of a triangle in the ratio 1:2:3 find the measure of each angle

Answer 1

Solution :

⏭ Given:

✏ Angles of a triangles in the ratio 1:2:3

⏭ To Find:

✏ The measure of each angle

⏭ Concept:

✏ We know that sum of all three angles of triangle is always 180°

$\bigstar \: \underline{ \boxed{ \bold{ \sf{ \pink{ \large{ \sum{(angles)} = 180 \degree}}}}}} \: \bigstar$

⏭ Calculation:

✏ Angle of triangle is given by

• ∠A = x
• ∠B = 2x
• ∠C = 3x

$\implies \sf \: \red{\angle{A} + \angle{B} + \angle{C} = 180 \degree} \\ \\ \implies \sf \: x + 2x + 3x = 180 \degree \\ \\ \implies \sf \: 6x = 180 \degree \\ \\ \implies \sf \: \purple{x = 30} \\ \\ \bigstar \boxed{ \green{ \angle{A} = x = 30 \degree}} \\ \\ \bigstar \: \boxed{ \blue{ \angle{B} = 2x = 60 \degree}} \\ \\ \bigstar \: \boxed{ \orange{ \angle{C} = 3x = 90 \degree}}$

⏭ Additional information:

• It is right angle triangle.

Answer 2

Solution -

________________________

Given-

Angles of a triangles in the ratio 1:2:3

________________________

To Find-

The measure of each angle

________________________

We know,

The sum of all angles of a ∆ = 180°

Let the angles be -

∠A = x

∠B = 2x

∠C = 3x

________________________

Solving-

➠∠A+∠B+∠C=180°

➠x+2x+3x=180°

➠6x=180°

➠x=30

________________________

∠A=x=30°

∠B=2x => 2×30 = 60°

∠C=3x => 3×30 = 90°

________________________