(C) Two angles are said to be complementary if their sum is $90^{\circ}$.Given that $\angle A + \angle B = 90^{\circ}$.Also,the ratio $\angle A : \ang

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$\angle A = 15^{\circ}, \angle B = 75^{\circ}$

(C) Two angles are said to be complementary if their sum is $90^{\circ}$.Given that $\angle A + \angle B = 90^{\circ}$.Also,the ratio $\angle A : \angle B = 1 : 5$. Let $\angle A = x$ and $\angle B = 5x$.Substituting these into the sum equation: $x + 5x = 90^{\circ}$.$6x = 90^{\circ}$.$x = 90^{\circ} / 6 = 15^{\circ}$.Therefore,$\angle A = 15^{\circ}$ and $\angle B = 5 \times 15^{\circ} = 75^{\circ}$.

Class 9 Mathematics Lines and Angles Pairs of Angles

Medium

$\angle A$ and $\angle B$ are complementary angles. If $\angle A : \angle B = 1 : 5$,then find $\angle A$ and $\angle B$.

A
$\angle A = 30^{\circ}, \angle B = 80^{\circ}$
B
$\angle A = 30^{\circ}, \angle B = 50^{\circ}$
C
$\angle A = 15^{\circ}, \angle B = 75^{\circ}$
D
$\angle A = 25^{\circ}, \angle B = 70^{\circ}$

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Lines and Angles

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Pairs of Angles

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

Easy

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$\angle APC$ and $\angle BPD$ are vertically opposite angles. If $\angle APC = 3x - 20^{\circ}$ and $\angle BPD = 2x + 30^{\circ}$,then find $x$ and the measure of both angles.

Medium

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$\angle ABD$ and $\angle DBC$ are adjacent angles. If $\angle ABD = 1.5x^{\circ}$,$\angle DBC = 2x^{\circ}$,and $\angle ABC = 70^{\circ}$,then find $x$ and the measures of $\angle ABD$ and $\angle DBC$.

Medium

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$\angle PQR$ and $\angle PQS$ are a linear pair of angles. If $11 \angle PQR = 9 \angle PQS$,then find $\angle PQR$ and $\angle PQS$.

Medium

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$\angle ABC$ and $\angle ABD$ are a linear pair of angles. If $\angle ABC : \angle ABD = 17 : 13$,then find $\angle ABC$ and $\angle ABD$.

Medium

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$\angle A$ and $\angle B$ are complementary angles. If $\angle A : \angle B = 1 : 5$,then find $\angle A$ and $\angle B$.

Similar Questions

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

$\angle APC$ and $\angle BPD$ are vertically opposite angles. If $\angle APC = 3x - 20^{\circ}$ and $\angle BPD = 2x + 30^{\circ}$,then find $x$ and the measure of both angles.

$\angle ABD$ and $\angle DBC$ are adjacent angles. If $\angle ABD = 1.5x^{\circ}$,$\angle DBC = 2x^{\circ}$,and $\angle ABC = 70^{\circ}$,then find $x$ and the measures of $\angle ABD$ and $\angle DBC$.

$\angle PQR$ and $\angle PQS$ are a linear pair of angles. If $11 \angle PQR = 9 \angle PQS$,then find $\angle PQR$ and $\angle PQS$.

$\angle ABC$ and $\angle ABD$ are a linear pair of angles. If $\angle ABC : \angle ABD = 17 : 13$,then find $\angle ABC$ and $\angle ABD$.

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