Question : The vertical angle $\angle A$ of an isosceles $\triangle ABC$ is three times the angle B on it. The measure of the $\angle A$ is:
Option 1: 90°
Option 2: 108°
Option 3: 100°
Option 4: 36°
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: 108°
Solution : Given: $\angle BAC$ of an isosceles $\triangle ABC$ is three times $\angle ABC$. In an isosceles $\triangle ABC$, $AB = AC$. $\angle B=\angle C$ $\angle A=3\angle B$ $\angle B =\angle C = \frac{\angle A}{3}$ We know that the sum of all the angles in a triangle is 180°. $\angle A+\angle B+\angle C=180°$ According to the question, $\angle A+\frac{\angle A}{3}+\frac{\angle A}{3}=180°$ $⇒\frac{3\angle A+\angle A+\angle A}{3}=180°$ $⇒5\angle A=540°$ $⇒\angle A=108°$ The measure of the $\angle A$ is 108°. Hence, the correct answer is 108°.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : ABC is an isosceles triangle such that AB = AC, $\angle$ABC = 55°, and AD is the median to the base BC. Find the measure of $\angle$BAD.
Question : In an isosceles $\triangle ABC$, AD is the median to the unequal side BC meeting at D, DP is the angle bisector of $\angle ADB$ and PQ is drawn parallel to BC meeting AC at Q. Then, the measure of $\angle PDQ$ is:
Question : In an isosceles $\triangle ABC$, $AB = AC$, $XY || BC$. If $\angle A=30°$, then $\angle BXY$?
Question : G is the centroid of $\triangle$ABC. If AG = BC, then measure of $\angle$BGC 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:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile