(A) Two angles are supplementary if their sum is $180^{\circ}$.Given $\angle X : \angle Y = 23 : 13$,let $\angle X = 23k$ and $\angle Y = 13k$.Since t

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$\angle X = 115^{\circ}, \angle Y = 65^{\circ}$

(A) Two angles are supplementary if their sum is $180^{\circ}$.Given $\angle X : \angle Y = 23 : 13$,let $\angle X = 23k$ and $\angle Y = 13k$.Since they are supplementary,$23k + 13k = 180^{\circ}$.$36k = 180^{\circ}$.$k = \frac{180^{\circ}}{36} = 5^{\circ}$.Therefore,$\angle X = 23 \times 5^{\circ} = 115^{\circ}$ and $\angle Y = 13 \times 5^{\circ} = 65^{\circ}$.

Class 9 Mathematics Lines and Angles Mix Examples - Lines and Angles

Medium

$\angle X$ and $\angle Y$ are supplementary angles. If $\angle X : \angle Y = 23 : 13$,then find $\angle X$ and $\angle Y$.

A
$\angle X = 115^{\circ}, \angle Y = 65^{\circ}$
B
$\angle X = 125^{\circ}, \angle Y = 55^{\circ}$
C
$\angle X = 105^{\circ}, \angle Y = 75^{\circ}$
D
$\angle X = 135^{\circ}, \angle Y = 45^{\circ}$

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Mix Examples - Lines and Angles

State whether each of the following statements is true or false:
$(1)$ The maximum number of right angles in any triangle is two.
$(2)$ The supplementary angle of the complementary angle of an angle having measure $33^{\circ}$ has measure $123^{\circ}$.

Medium

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If in the figure,bisectors $AP$ and $BQ$ of the alternate interior angles are parallel,then show that $l \parallel m$.

Medium

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$\angle A$ and $\angle B$ are complementary angles. If $\angle A = \angle B - 20^{\circ}$,then find $\angle A$ and $\angle B$.

Medium

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In the figure,$OD$ is the bisector of $\angle AOC$,$OE$ is the bisector of $\angle BOC$,and $OD \perp OE$. Show that the points $A, O$,and $B$ are collinear.

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In the given figure,if $AB \parallel CD$,$\angle AXY = 80^{\circ}$ and $\angle XZD = 140^{\circ}$,then find $x$ and $y$.

Medium

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$\angle X$ and $\angle Y$ are supplementary angles. If $\angle X : \angle Y = 23 : 13$,then find $\angle X$ and $\angle Y$.

Similar Questions

State whether each of the following statements is true or false:$(1)$ The maximum number of right angles in any triangle is two.$(2)$ The supplementary angle of the complementary angle of an angle having measure $33^{\circ}$ has measure $123^{\circ}$.

If in the figure,bisectors $AP$ and $BQ$ of the alternate interior angles are parallel,then show that $l \parallel m$.

$\angle A$ and $\angle B$ are complementary angles. If $\angle A = \angle B - 20^{\circ}$,then find $\angle A$ and $\angle B$.

In the figure,$OD$ is the bisector of $\angle AOC$,$OE$ is the bisector of $\angle BOC$,and $OD \perp OE$. Show that the points $A, O$,and $B$ are collinear.

In the given figure,if $AB \parallel CD$,$\angle AXY = 80^{\circ}$ and $\angle XZD = 140^{\circ}$,then find $x$ and $y$.

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State whether each of the following statements is true or false:
$(1)$ The maximum number of right angles in any triangle is two.
$(2)$ The supplementary angle of the complementary angle of an angle having measure $33^{\circ}$ has measure $123^{\circ}$.