In the following figure,ray YW stands on a li | vedclass

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

Question

(A) Since ray $YW$ stands on line $XYZ$,$\angle WYZ + \angle WYX = 180^{\circ}$ (Linear pair of angles).Given that $\angle WYZ : \angle WYX = 1 : 2$,l

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(A) Since ray $YW$ stands on line $XYZ$,$\angle WYZ + \angle WYX = 180^{\circ}$ (Linear pair of angles).Given that $\angle WYZ : \angle WYX = 1 : 2$,let $\angle WYZ = x$ and $\angle WYX = 2x$.Therefore,$x + 2x = 180^{\circ} \implies 3x = 180^{\circ} \implies x = 60^{\circ}$.So,$\angle WYZ = 60^{\circ}$ and $\angle WYX = 120^{\circ}$.Ray $YQ$ is the angle bisector of $\angle WYZ$,so $\angle WYQ = \frac{1}{2} 	imes \angle WYZ = \frac{1}{2} 	imes 60^{\circ} = 30^{\circ}$.Ray $YP$ is the angle bisector of $\angle WYX$,so $\angle WYP = \frac{1}{2} 	imes \angle WYX = \frac{1}{2} 	imes 120^{\circ} = 60^{\circ}$.Finally,$\angle PYQ = \angle WYQ + \angle WYP = 30^{\circ} + 60^{\circ} = 90^{\circ}$.

In the following figure,ray $YW$ stands on a line $XYZ$. $\angle WYZ : \angle WYX = 1 : 2$. Ray $YQ$ and ray $YP$ are angle bisectors of $\angle WYZ$ and $\angle WYX$ respectively. Find $\angle PYQ$. (in $^{\circ}$)

Similar Questions

$\angle A$ and $\angle B$ are supplementary angles. If $\angle A : \angle B = 3 : 7$,then $\angle B = \dots$ (in $^o$)

In the following figure,lines $AB$ and $CD$ intersect each other at point $P$. If $\angle APC : \angle BPC = 7 : 8$,find all the angles.

Let $OA, OB, OC$ and $OD$ be rays in the anticlockwise direction such that $\angle AOB = 100^{\circ}, \angle COD = 100^{\circ}, \angle BOC = 82^{\circ}$ and $\angle AOD = 78^{\circ}$. Is it true to say that $AOC$ and $BOD$ are lines?

In the given figure,$AB \parallel DE$ and $BC \parallel EF$. Prove that $\angle ABC + \angle DEF = 180^{\circ}$.

In the given figure,$AB \parallel DE$ and $BC \parallel EF$. Prove that $\angle ABC = \angle DEF$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module