Question

in a right angled triangle the accute angles are (2x-20) ° and (4x+20) ° , find all the angles of the triangle​

Answer 1

Answer :-

• The angles of the right angled triangle are 10°, 80° and 90°.

Given :-

• The acute angles of the right angled triangle are (2x - 20)° and (4x + 20)°.

To find :-

• All the angles of the triangle.

Step-by-step explanation :-

We know that one angle of a right angled triangle is 90°.

We also know that the other two acute angles are (2x - 20)° and (4x + 20)°.

The sum of all the angles of a triangle = 180°.

Thus, we get :-

$\sf (2x - 20)^{\circ} + (4x + 20)^{\circ} + 90^{\circ} = 180^{\circ}$

$\sf 2x^{\circ} - 20^{\circ} + 4x^{\circ} + 20^{\circ} + 90^{\circ} = 180^{\circ}$

$\sf 2x^{\circ} + 4x^{\circ} - 20^{\circ} + 20^{\circ} + 90^{\circ} = 180^{\circ}$

$\sf 6x^{\circ} + 90^{\circ} = 180^{\circ}$

$\sf 6x^{\circ} = 180^{\circ} - 90^{\circ}$

$\sf 6x^{\circ} = 90^{\circ}$

$\sf x = \dfrac{90}{6}$

$\sf x = 15^{\circ}.$

We now know that x = 15°.

So, the other two angles are :-

(2x - 20)° = 2° × 15° - 20° = 30° - 20° = 10°.

(4x + 20)° = 4° × 15° + 20° = 60° + 20° = 80°.

Thus, the three angles of the right angled triangle are 10°, 80° and 90°.

Verification :-

To check our answer, we just have to add all the angles and see if we get 180° or not.

10° + 80° + 90° = 90° + 90° = 180°.

$\sf \bf Since\:the\:sum\:of\:all\:the\:angles=180^{\circ},$

$\sf \bf Hence\:verified.$

Answer 2

90∘ ,35∘ and 55∘

Explanation:

Let the 2 angles be x and x + 20

⇒x + x + 20∘ +90 ∘ = 180∘ [Angles Sum Property]

⇒2x + 110∘ = 180∘

⇒2x = 70∘

⇒x = 35∘

So,

The 2 angles are x = 35∘ & x + 20∘ = 55∘

That gives us the 3 angles: 90∘ 35∘ and 55∘

Verification:

90∘ + 35∘ + 55∘

=180∘ [As per the Angle Sum Property]

Note - " ∘ " This is called degree.