Question : If $ABCD$ is a cyclic quadrilateral with $\angle A=50^{\circ},\angle B=80^{\circ}$, then $\angle C$ and $ \angle D$ are:
Option 1: $100^{\circ}$ and $130^{\circ}$
Option 2: $115^{\circ}$ and $115^{\circ}$
Option 3: $110^{\circ}$ and $120^{\circ}$
Option 4: $130^{\circ}$ and $100^{\circ}$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $130^{\circ}$ and $100^{\circ}$
Solution : In a cyclic quadrilateral, the sum of each pair of opposite angles is $180^{\circ}$. $⇒\angle A + \angle C = 180^{\circ}$ $⇒\angle B + \angle D = 180^{\circ}$ Given that $\angle A = 50^{\circ}$ and $\angle B = 80^{\circ}$ $\therefore\angle C = 180^{\circ} - \angle A = 180^{\circ} - 50^{\circ} = 130^{\circ}$ $\therefore \angle D = 180^{\circ} - \angle B = 180^{\circ} - 80^{\circ} = 100^{\circ}$ Hence, the correct answer is $130^{\circ}$ and $100^{\circ}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : ABCD is a cyclic quadrilateral in which angle B is opposite to angle D. If $\angle \mathrm{B}=(\mathrm{x}+10)^{\circ}$ and $\angle \mathrm{D}=(2 \mathrm{x}+35)^{\circ}$, then what is the value of $\mathrm{x}$?
Question : In a cyclic quadrilateral ABCD. $\angle {A}$ is opposite to $\angle {C}$. If $\angle {A}=110°$, then what is the value of $\angle {C}$?
Question : In $\triangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$. If $\angle A = 80^\circ$, then $\angle BOC$ is equal to:
Question : ABCD is a cyclic quadrilateral, AB is the diameter of the circle. If angle $\angle ACD=45^{\circ}$, then what is the value of $\angle BAD$?
Question : In a triangle ABC, two angles A and B are equal. If the exterior angle is at $\angle A = 115°$, find the measure of $\angle C$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile