Question

one angle of a triangle is 65 degree . Find the remaining two angles if their difference is 20 degree​

Answer 1

Answer:

Step-by-step explanation:

Given,

One of the angle is 65°

Let other angle be x

And another angle be x-20

According to Angle Sum property of Triangle ,

➡️ 65° + x + x-20° = 180°

➡️ 45° +2x = 180°

➡️ 2x = 180-45°

➡️ 2x = 135°

➡️ X = 135/2

➡️x = 67.5°

Therefore other angles are ,

x = 67.5°

x - 20 = 67.5-20 =47.5°

Answer 2

$\large{\mathfrak{\underline{\underline{Answer:-}}}}$

x = 67.5°

y = 47.5°

${\mathfrak{\underline{\underline{Step-By-Step-Explanation:-}}}}$

Given :-

One angle of a triangle is 65° .

Sum of other two angles is 20°.

____________________________

To find :-

Other two angles.

____________________________

Solution :-

Let the other two angles be x and y respectively.

So,

x - y = 20°

⟹ x = 20°+ y ............(1)

⟹ y = x - 20°...............(2)

___________________________

ATQ,

x + y + 65° = 180° [Angle sum Property]

Substitute values of x from (1)

__________

We have,

65 + y + 20 + y = 180°

[Angle Sum Property]

⟹ 2y = 180 - 20 -65

2y = 95

⟹ y = 95/2

y =47.5°.............(3)

$\large{\star{\boxed{\boxed{y \: = \: 47.5^{\circ}}}}}$

Substitute value of y in (1)

x - 47.5° = 20°

x = 20 + 47.5

x = 67.5°

$\large{\star{\boxed{\boxed{x \: = \: 67.5^{\circ}}}}}$

$\rule{200}{2}$

Angle Sum Property of a Triangle :-

It state that Sum of all the three angles of a triangle is 180°.

$\rule{200}{2}$