In the figure,two line segments AC and BD int | vedclass

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

Question

(C) In $	riangle APB$ and $	riangle DPC$,we have:$\angle APB = \angle DPC = 50^{\circ}$ [Vertically opposite angles]Now,consider the ratios of the s

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) In $	riangle APB$ and $	riangle DPC$,we have:$\angle APB = \angle DPC = 50^{\circ}$ [Vertically opposite angles]Now,consider the ratios of the sides including the equal angles:$\frac{PA}{PD} = \frac{6}{5} = 1.2$$\frac{PB}{PC} = \frac{3}{2.5} = \frac{30}{25} = 1.2$Since $\frac{PA}{PD} = \frac{PB}{PC}$ and the included angles are equal,by the $SAS$ similarity criterion:$	riangle APB \sim 	riangle DPC$Since the triangles are similar,their corresponding angles are equal:$\angle PAB = \angle PDC = 30^{\circ}$In $	riangle APB$,the sum of angles is $180^{\circ}$:$\angle PAB + \angle APB + \angle PBA = 180^{\circ}$$30^{\circ} + 50^{\circ} + \angle PBA = 180^{\circ}$$80^{\circ} + \angle PBA = 180^{\circ}$$\angle PBA = 180^{\circ} - 80^{\circ} = 100^{\circ}$

In the figure,two line segments $AC$ and $BD$ intersect each other at the point $P$ such that $PA = 6 \, cm$,$PB = 3 \, cm$,$PC = 2.5 \, cm$,$PD = 5 \, cm$,$\angle APB = 50^{\circ}$ and $\angle CDP = 30^{\circ}$. Then,$\angle PBA$ is equal to: (in $^{\circ}$)

Similar Questions

Prove that the sum of squares of the sides of a rectangle is equal to the sum of squares of its diagonals.

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is an altitude to the hypotenuse $\overline{AC}$. If $AM = 12$ and $CM = 3$,then $BM = \dots$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BE}$ is a median. If $AB = 3.6$ and $BC = 4.8$,find $BE$.

Find the value of $x$ for which $DE \parallel AB$ in the given figure.

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $\overline{BD}$ is an altitude to the hypotenuse $AC$. If $AD = 9$ and $CD = 4$,find $BD$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module