Question : In $\triangle {ABC}$, D is a point on BC such that $\angle {ADB}=2 \angle {DAC}, \angle {BAC}=70^{\circ}$ and $\angle {B}=56^{\circ}$. What is the measure of $\angle A D C$?
Option 1: $72^{\circ}$
Option 2: $54^{\circ}$
Option 3: $74^{\circ}$
Option 4: $81^{\circ}$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $72^{\circ}$
Solution :
Let $\angle DAC = x$ $\angle ADB = 2x$ $\angle BAC = 70^\circ$ $\angle BAD = 70^\circ - x$ In $\triangle ABD $ $⇒56^\circ + 2x^\circ + 70^\circ - x = 180^\circ $ $⇒ x = 54^\circ$ $⇒2x = 108^\circ$ Now, By linear pair of angles $\angle ADB + \angle ADC = 180^\circ $ $⇒ 2x + \angle ADC = 180^\circ$ $⇒ 108^\circ + \angle ADC = 180^\circ $ $⇒ \angle ADC = 180^\circ - 108^\circ$ $⇒ \angle ADC = 72^\circ$ Hence, the correct answer is $72^\circ$.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : In a triangle ${ABC}, {D}$ is a point on ${BC}$ such that $\frac{A B}{A C}=\frac{B D}{D C}$. If $\angle B=68^{\circ}$ and $\angle C=52^{\circ}$, then measure of $\angle B A D$ is equal to:
Question : In $\triangle $ABC, D is a point on side BC such that $\angle$ADC = 2$\angle$BAD. If $\angle$A = 80° and $\angle$C = 38°, then what is the measure of $\angle$ADB?
Question : If O is the orthocenter of a triangle ABC and $\angle$ BOC = 100$^\circ$, then the measure of $\angle$BAC is ____.
Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:
Question : In $\triangle A B C, \angle B=78^{\circ}, A D$ is a bisector of $\angle A$ meeting BC at D, and $A E \perp B C$ at $E$. If $\angle D A E=24^{\circ}$, then the measure of $\angle A C B$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile