Lines AB and CD intersect at P. If angle APC | vedclass

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

Question

(A) When two lines intersect,the vertically opposite angles are equal.Since lines $AB$ and $CD$ intersect at $P$,$\angle APC$ and $\angle BPD$ are ver

Vedclass · Accepted Answer

$x = 25, \angle APC = 80^{\circ}, \angle BPD = 80^{\circ}$

Vedclass · Answer

(A) When two lines intersect,the vertically opposite angles are equal.Since lines $AB$ and $CD$ intersect at $P$,$\angle APC$ and $\angle BPD$ are vertically opposite angles.Therefore,$\angle APC = \angle BPD$.Substituting the given expressions: $2x + 30^{\circ} = 4x - 20^{\circ}$.Rearranging the terms: $30^{\circ} + 20^{\circ} = 4x - 2x$.$50^{\circ} = 2x$,which gives $x = 25^{\circ}$.Now,calculate the angles:$\angle APC = 2(25) + 30 = 50 + 30 = 80^{\circ}$.$\angle BPD = 4(25) - 20 = 100 - 20 = 80^{\circ}$.Thus,$x = 25$,$\angle APC = 80^{\circ}$,and $\angle BPD = 80^{\circ}$.

Lines $AB$ and $CD$ intersect at $P$. If $\angle APC = 2x + 30^{\circ}$ and $\angle BPD = 4x - 20^{\circ}$,then find $x$,$\angle APC$,and $\angle BPD$.

Similar Questions

Prove that the sum of the three angles of a triangle is $180^{\circ}$.

An angle has a measure equal to $\frac{5}{4}$ of the measure of its complementary angle. Find the measure of that angle. (in $^o$)

In the figure,$BA \parallel ED$ and $BC \parallel EF.$ Show that $\angle ABC = \angle DEF.$

An exterior angle of a triangle is $105^{\circ}$ and its two interior opposite angles are equal. Each of these equal angles is

$\angle ACD$ is an exterior angle of $\Delta ABC$. If $\angle A = 70^{\circ}$ and $\angle B = 40^{\circ}$ in $\Delta ABC$,then find $\angle ACD$. (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module