Question

Two angles of a triangle are in the ratio 4:5.If the sum of these angles is equal to the third angle,find the angles of the triangle.​

Answer 1

Answer:

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Step-by-step explanation:

Let the triangle (Δ) be ABC

Given : ∠A = 4x

∠B = 5x

∠C = ∠A+∠B

∠C= 4x + 5x = 9x

                                              

Here we use angle sum property

⇒ ∠A + ∠B + ∠C = 180°

⇒ 4x + 5x + 9x

⇒ 18x = 180°

⇒ x =

⇒ x = 10°

                                              

Let us verify that

to verify our answer  we have to put 10°  at the place of 'x'

let's do that

                                            

⇒  ∠A + ∠B + ∠C = 180°

⇒ 4x + 5x + 9x  = 180°

⇒ 4×10 + 5×10 + 9×10 = 180°

⇒ 40 + 50 + 90 = 180°

⇒ 90 + 90 = 180°

⇒ 180°  = 180°

                                          

∠A = 4x  = 4×10 = 40°

∠B = 5x  = 5×10 = 50°

∠C = ∠A+∠B

∠C= 4x + 5x = 9x  = 9×10 = 90°

                                            

Therefore angles of triangle are 40° , 50°  and 50°

Answer 2

Let the measure of two angles be 4x and 5x and the third one is ( 4x + 5x ).

We know that ;

Sum of angles of triangle = 180°

⇒ 4x + 5x + 4x + 5x = 180

⇒ 18x = 180

⇒ x = 180/18

⇒ x = 10

Therefore, the angles are ;

4x = 4 * 10 = 40°

5x = 5 * 10 = 50°

9x = 9 * 10 = 90°