Question
In a cyclic quadrilateral ABCD if AB || CD and $\angle\text{B}=70^\circ,$ find the remaining angles.
✓
Answer
We have, $\angle\text{B}=70^\circ$Since, ABCD is a cyclic quadrilateral
Then, $\angle\text{B}+\angle\text{D}=180^\circ$
$\Rightarrow70^\circ+\angle\text{D}=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-70^\circ=110^\circ$
Since, AB || DC
Then, $\angle\text{B}+\angle\text{C}=180^\circ$ [Co-interior angles]
$\Rightarrow70^\circ+\angle\text{C}=180^\circ$
$\Rightarrow\angle\text{C}=180^\circ-70^\circ=110^\circ$
Now, $\angle\text{A} +\angle\text{C}=180^\circ$ [Opposite angles of cyclic quad.]
$\Rightarrow\angle\text{A}+110^\circ=180^\circ$
$\Rightarrow\angle\text{A}=180^\circ-110^\circ=70^\circ$
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 cube of the following binomial expressions:$\frac{3}{\text{x}}-\frac{2}{\text{x}^2}$
→In the given figure, BA || ED and BC || EF. Show that $\angle\text{ABC}+\angle\text{DEF}=180^\circ.$
→Plot the following points on the graph paper:(-4, 0)
Construct $\triangle \mathrm{DEF}$ such that $\mathrm{DE}=4.2 \mathrm{~cm}, \angle \mathrm{D}=60^{\circ}, \angle \mathrm{E}=70^{\circ}$ and draw circumcircle of it. Draw rough figure. Write the given measures.
→In right angled $\triangle P Q R, \angle Q=90^{\circ}, \angle R=\theta$ and if $\sin \theta=\frac{5}{13}$, then find $\cos \theta$ and $\tan \theta$,
→The vertex A of $\triangle\text{ABC}$ is joined to a point D on the side BC. The mid-point of AD is E.
Prove that $\text{ar}(\triangle\text{BEC})=\frac{1}{2}\text{ar}(\triangle\text{ABC}).$
→Prove that $\text{ar}(\triangle\text{BEC})=\frac{1}{2}\text{ar}(\triangle\text{ABC}).$
Factorize the following expressions:$\Big[\frac{\text{x}}{2}+\text{y}+\frac{\text{z}}{3}\Big]^3+\Big[\frac{\text{x}}{3}-\frac{2\text{y}}{3}+\text{z}\Big]^3+\Big[-\frac{5\text{x}}{6}-\frac{\text{y}}{3}-\frac{4\text{z}}{3}\Big]^3$
→Write the following pairs considering □ABCD.
Find the value of $\frac{6}{\sqrt5-\sqrt3},$ it being given that $\sqrt3=1.732$ and $\sqrt5=2.236.$
→Visualise $2.665$ on the number line, using successive magnification.
→