If one angle of a parallelogram is 24° less than twice the . . .

Question : If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of a parallelogram is :

(a) 176°

(b) 68°

(d) 102°

Doubt by Noor

Solution :

Let the smallest angle of the parallelogram be x and the largest angle be y

We also know that in parallelogram opposite angles are equal to each other and adjacent angles are supplementary (180°).

ATQ
y=2x-24° — (1)

x+y=180° (Sum of adjacent angles of a parallelogram)

x+2x-24°=180° [From Equation (1)]
3x-24°=180°
3x=180°+24°
3x=204°
x=204°/3
x=68°

Substituting in equation (1)

y=2(68°)-24°
y=136°-24
y=112°

The largest angle of the parallelogram is 112°.

Hence, (c) 112°, would be the correct option.

Class 9