Question
In the given figure, $BAD\ ||\ EF$, $\angle\text{AEF}=55^\circ$ and $\angle\text{ACB}=25^\circ,$ find $\angle\text{ABC}.$ 
✓
Answer
$BAD\ ||\ EF$ and $EC$ is the transversal.
$\Rightarrow\angle\text{AEF}=\angle\text{CAD}$ (corresponding angles)
$\Rightarrow\angle\text{CAD}=55^\circ$ Now,
$\angle\text{CAD}+\angle\text{CAB}=180^\circ$ (linear pair)
$\Rightarrow55^\circ+\angle\text{CAB}=180^\circ$
$\Rightarrow\angle\text{CAB}=125^\circ$ In $\triangle\text{ABC},$
by angle sum property, $\angle\text{ABC}+\angle\text{CAB}+\angle\text{ACB}=180^\circ$
$\Rightarrow\angle\text{ABC}+125^\circ+25^\circ=180^\circ$
$ \Rightarrow\angle\text{ABC}=30^\circ$
$\Rightarrow\angle\text{AEF}=\angle\text{CAD}$ (corresponding angles)
$\Rightarrow\angle\text{CAD}=55^\circ$ Now,
$\angle\text{CAD}+\angle\text{CAB}=180^\circ$ (linear pair)
$\Rightarrow55^\circ+\angle\text{CAB}=180^\circ$
$\Rightarrow\angle\text{CAB}=125^\circ$ In $\triangle\text{ABC},$
by angle sum property, $\angle\text{ABC}+\angle\text{CAB}+\angle\text{ACB}=180^\circ$
$\Rightarrow\angle\text{ABC}+125^\circ+25^\circ=180^\circ$
$ \Rightarrow\angle\text{ABC}=30^\circ$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the median of the data: $92, 35, 67, 85, 72, 81, 56, 51, 42, 69$
→A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water up to $1\ cm$ from the top.
When a solid cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows.
Calculate the volume of the cube and also the length of its edge.
→When a solid cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows.
Calculate the volume of the cube and also the length of its edge.
A traffic signal board, indicating $\text{SCHOOLAHEAD}$ is an equilateral triangle with side a Find the area of the signal board, using Heron's formula. If its perimeter is $180 \ cm$, what will be the area of the signal board?
→If $x=1$ and $y=6$ is a solution of the equation $8 x-a y+a^2=0$, find the values of $a$.
→Simplify: $\frac{1}{\sqrt{3}+\sqrt{2}}-\frac{2}{\sqrt{5}-\sqrt{3}}-\frac{3}{\sqrt{2}-\sqrt{5}}$
→Factorize the following expressions: $\frac{1}{27}\text{x}^3-\text{y}^3+125\text{z}^3+5\text{xyz}$
→The mean of $12$ numbers is $40$. If each numbers is divided by $8$, what will be the mean of the new numbers?
→In figure, $ABCD$ is a parallelogram in which $\angle\text{DAB}=75^\circ$ and $\angle\text{DBC}=60^\circ$.
Compute $\angle\text{CDB},$ and $\angle\text{ADB}$.
→Compute $\angle\text{CDB},$ and $\angle\text{ADB}$.
Give the geometric representations of the following equations:
$a.$ On the number line.
$b.$ On the Cartesain plane.
$x = 2$
→$a.$ On the number line.
$b.$ On the Cartesain plane.
$x = 2$
In given $\text{l}\ ||\ \text{m}$ and $M$ is the mid-point of a line segment $AB$. Show that $M$ is also the mid-point of any line segment $CD$, having its end points on $l$ and $m$, respectively.
→