In the figure,if PQ parallel RS,angle MXQ = 1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) To solve this,we draw a line $AB$ passing through point $M$ such that $AB \parallel PQ$. Since $PQ \parallel RS$ and $AB \parallel PQ$,it follows

Vedclass · Accepted Answer

$85$

Vedclass · Answer

(B) To solve this,we draw a line $AB$ passing through point $M$ such that $AB \parallel PQ$. Since $PQ \parallel RS$ and $AB \parallel PQ$,it follows that $AB \parallel RS$.Now,consider the transversal $XM$ intersecting parallel lines $PQ$ and $AB$. The interior angles on the same side of the transversal are supplementary.Therefore,$\angle QXM + \angle XMB = 180^o$.Given $\angle QXM = 135^o$,we have $135^o + \angle XMB = 180^o$,which gives $\angle XMB = 180^o - 135^o = 45^o$ (Equation $1$).Next,consider the transversal $YM$ intersecting parallel lines $RS$ and $AB$. The alternate interior angles are equal.Therefore,$\angle BMY = \angle MYR$.Given $\angle MYR = 40^o$,we have $\angle BMY = 40^o$ (Equation $2$).Finally,$\angle XMY = \angle XMB + \angle BMY$.Substituting the values from Equation $1$ and Equation $2$,we get $\angle XMY = 45^o + 40^o = 85^o$.

In the figure,if $PQ \parallel RS$,$\angle MXQ = 135^o$ and $\angle MYR = 40^o$,find $\angle XMY$. (in $^o$)

Similar Questions

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel,then prove that the two lines are parallel.

In the figure,if $PQ \parallel ST$,$\angle PQR = 110^o$ and $\angle RST = 130^o$,find $\angle QRS$. (in $^o$)

In the figure,$PQ$ and $RS$ are two mirrors placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B$,the reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD$. Prove that $AB \parallel CD$.

In the figure,find the values of $x$ and $y$ and then show that $AB \parallel CD$.

In the figure,$POQ$ is a line. Ray $OR$ is perpendicular to line $PQ$. $OS$ is another ray lying between rays $OP$ and $OR$. Prove that $\angle ROS = \frac{1}{2}(\angle QOS - \angle POS)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module