Question

The sum of two angels is equal to 90 degree. The ratio of the measures of these angles is 4 : 5. What are the measures of these two angles. ​

Answer 1

Answer: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°

hope it helps u

follow me

Answer 2

$\huge\bold{Answer:-}$

Given:-

• The sum of the angles is 90°
• The angles are in the ratio 4:5

To Find:-

• The measures of the angles

$\huge\bold{★Solution:-★}$

Let, the angles be 4x , 5x

ATQ

⟼ 4x + 5x = 90°

⟼ 9x = 90°

⟼ x = $\dfrac{90°}{9}$

⟼ x = 10°

so, the measure of the angles be

4x.

= 4 × 10°

= 40°

5x

= 5 × 10°

= 50°

Therefore , the measure of the two angles are 40° and 50° .