Question

Larger of two supplementary angles exceeds the smaller 18 degrees.Find them
Class 10 Ch 3​

Answer 1

GiveN :

• Two angles are supplementary
• Larger Angle exceeds other by 18°

To FinD :

• Measure of angles

SolutioN :

let smaller angle be x, then larger will be x + 18°

A.T.Q,

⇒x + x + 18° = 180°

⇒2x + 18° = 180°

⇒2x = 180° - 18°

⇒2x = 162

⇒x = 162/2

⇒x = 81°

• Smaller angle = x = 81°
• Bigger angle = x + 18° = 81° + 18° = 99°

$\rule{200}{2}$

Verification :

If the angles are supplementary then there sum should be 180°

⇒81° + 99°

⇒180° = 180°

• So, our answer is correct

Answer 2

$\huge\underline\mathrm{GivEn:-}$

⭐ Two angles are supplementary

⭐ The smaller exceeds the larger angle by 18°.

$\huge\underline\mathrm{Need\: To\: Find:-}$

↔ Find the angles = ?

$\huge\underline\mathrm{soLution:-}$

Let the smaller angle be 'x'

and larger be x + 18

According to Question :-

By angle sum property --

angle A + angleB + angleC = 180°

$\implies$ x + x + 18 = 180

$\implies$ 2x + 18 = 180

$\implies$ 2x = 180 - 18

$\implies$ 2x = 162

$\implies$ x = 81°

Smaller angle = 81°

Larger angle = 81+18=99°

$\huge\underline\mathrm{Verification:-}$

➡ According to angle sum property, the sum of all angles in a triangle is 180°

$\implies$ 99° + 81°= 180°

$\implies$ 180° = 180°

Verified✔...

$\huge\underline\mathrm{ThAnKs...}$