Class 9 Mathematics Lines and Angles Pairs of Angles

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For what value of $x+y$ in the figure will $ABC$ be a straight line? Justify your answer.

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Solution

(N/A) In the given figure,$x$ and $y$ are two adjacent angles formed at point $B$.
For $ABC$ to be a straight line,the sum of the adjacent angles $x$ and $y$ must be equal to $180^{\circ}$.
This is based on the linear pair axiom,which states that if a ray stands on a line,then the sum of two adjacent angles so formed is $180^{\circ}$.
Therefore,$x + y = 180^{\circ}$.

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Class 9 Questions

Class 9

Mathematics Questions

Chapter

Lines and Angles

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Pairs of Angles

In the following figure,in $\Delta ABC$,$\angle ABC = 70^{\circ}$ and $\angle ACB = 60^{\circ}$. Find $\angle ABD$ and $\angle ACE$.

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In the figure,the sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ respectively. If the bisectors $BO$ and $CO$ of $\angle CBE$ and $\angle BCD$ respectively meet at point $O$,then prove that $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.

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

Medium

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Ray $YM$ is the bisector of $\angle XYZ$ and ray $YN$ is the bisector of $\angle MYZ$. If $\angle XYN = 45^{\circ}$,then find $\angle XYZ$. (in $^{\circ}$)

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For what value of $x+y$ in the figure will $ABC$ be a straight line? Justify your answer.

Similar Questions

In the following figure,in $\Delta ABC$,$\angle ABC = 70^{\circ}$ and $\angle ACB = 60^{\circ}$. Find $\angle ABD$ and $\angle ACE$.

In the figure,the sides $AB$ and $AC$ of $\Delta ABC$ are produced to points $E$ and $D$ respectively. If the bisectors $BO$ and $CO$ of $\angle CBE$ and $\angle BCD$ respectively meet at point $O$,then prove that $\angle BOC = 90^o - \frac{1}{2} \angle BAC$.

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

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

Ray $YM$ is the bisector of $\angle XYZ$ and ray $YN$ is the bisector of $\angle MYZ$. If $\angle XYN = 45^{\circ}$,then find $\angle XYZ$. (in $^{\circ}$)

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