(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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State whether the following statement is true or false:
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The angles of a triangle are in the ratio $5:3:7$. The triangle is

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In the figure,$AB$,$CD$,and $EF$ are three lines concurrent at $O$. Find the value of $y$. (in $^{\circ}$)

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

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State whether each of the following statements is true or false:
$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.
$(2)$ The maximum number of acute angles in any triangle is two.

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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 the following statement is true or false:$(1)$ In $\Delta PQR$,$\angle P = \angle Q = 95^{\circ}$ is possible.

The angles of a triangle are in the ratio $5:3:7$. The triangle is

In the figure,$AB$,$CD$,and $EF$ are three lines concurrent at $O$. Find the value of $y$. (in $^{\circ}$)

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

State whether each of the following statements is true or false:$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.$(2)$ The maximum number of acute angles in any triangle is two.

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State whether the following statement is true or false:
$(1)$ In $\Delta PQR$,$\angle P = \angle Q = 95^{\circ}$ is possible.

State whether each of the following statements is true or false:
$(1)$ If a transversal intersects two parallel lines,then the interior angles on the same side of the transversal are equal.
$(2)$ The maximum number of acute angles in any triangle is two.