Question

The 3 inside angles A B and C of a right angled triangle are in the ratio of 7: 18: 11.
The smallest angle is 35°
Work out angles A B and C

Answer 1

In the above Question , the following information is given -

The three angles, A , B and C of a right angled Triangle are in a ratio of 7 : 18 : 11 .

We have to work out the values of Angles A , B and C

Solution -

We know that -

The three angles, A , B and C of a right angled Triangle are in a ratio of 7 : 18 : 11 .

So , let the angles , A , B and C be 7x , 18x and 11x respectively .

Now, from angle sum property , we know that -

Sum of all angles in a triangle = 180°

Hence

7x + 18x + 11x = 180°

=> 36x = 180°

=> x = 5°

Angle A

=> 7x

=> 7 × 5 °

=> 35°

Angle B

=> 18x

=> 18 × 5 °

=> 90°

Angle C

=> 11x

=> 11 × 5 °

=> 55°

Hence , the values of Angle A , angle B and angle C are 35° , 90° and 55° respectively .

___________

Answer 2

✯✯ QUESTION ✯✯

The 3 inside angles A B and C of a right angled triangle are in the ratio of 7: 18: 11. The smallest angle is 35° Work out angles A B and C..

━━━━━━━━━━━━━━━━━━━━

✰✰ ANSWER ✰✰

$\longmapsto\tt{Let\:Angle\:A\:be=7x}$

$\longmapsto\tt{Let\:Angle\:B\:be=18x}$

$\longmapsto\tt{Let\:Angle\:C\:be=11x}$

➙Sum of Angles of a Triangle is 180°

➥A.T.Q : -

$\longmapsto\tt{7x+18x+11x=180\degree}$

$\longmapsto\tt{32x=180\degree}$

$\longmapsto\tt{x=\cancel\dfrac{180}{32}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{x}\orange{=}\purple{5}}}$

➥Now ,

$\longmapsto\tt{Angle\:A=7(5)}$

$\longmapsto\tt{35\degree}$

$\longmapsto\tt{Angle\:B=18(5)}$

$\longmapsto\tt{90\degree}$

$\longmapsto\tt{Angle\:C=11(5)}$

$\longmapsto\tt{55\degree}$

_______________________

☛VERIFICATION : -

$\longmapsto\tt{35\degree+90\degree+55\degree=180\degree}$

$\longmapsto\tt{180\degree=180\degree}$

✺ HENCE VERIFIED ✺