(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 Mix Examples - Lines and 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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Mix Examples - Lines and Angles

Lines $AB$ and $CD$ intersect at $P$. If $\angle APC = 2x + 30^{\circ}$ and $\angle BPD = 4x - 20^{\circ}$,then find $x$,$\angle APC$,and $\angle BPD$.

Medium

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In the given figure,in $\Delta PQR$,$\angle Q > \angle R$. $PM \perp QR$ and $PA$ is the bisector of $\angle QPR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.

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If an angle is $20^{\circ}$ more than its complementary angle,then the measure of that angle is $\ldots \ldots \ldots$ (in $^{\circ}$)

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The supplementary angle of the complementary angle of an angle having measure $32^{\circ}$ has measure.......... (in $^{\circ}$)

Easy

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$\angle ACD$ is an exterior angle of $\Delta ABC$ and the bisector of $\angle A$ intersects $BC$ at $E$. Prove that $\angle ABC + \angle ACD = 2 \angle AEC$.

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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

Lines $AB$ and $CD$ intersect at $P$. If $\angle APC = 2x + 30^{\circ}$ and $\angle BPD = 4x - 20^{\circ}$,then find $x$,$\angle APC$,and $\angle BPD$.

In the given figure,in $\Delta PQR$,$\angle Q > \angle R$. $PM \perp QR$ and $PA$ is the bisector of $\angle QPR$. Prove that $\angle APM = \frac{1}{2}(\angle Q - \angle R)$.

If an angle is $20^{\circ}$ more than its complementary angle,then the measure of that angle is $\ldots \ldots \ldots$ (in $^{\circ}$)

The supplementary angle of the complementary angle of an angle having measure $32^{\circ}$ has measure.......... (in $^{\circ}$)

$\angle ACD$ is an exterior angle of $\Delta ABC$ and the bisector of $\angle A$ intersects $BC$ at $E$. Prove that $\angle ABC + \angle ACD = 2 \angle AEC$.

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