Math, asked by sinhabhagyasree4991, 9 months ago

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

Answers

Answered by Anonymous
10

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.
Answered by Anonymous
27

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°

________________________

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