Question : Three angles of a triangle are $(x-15^{\circ}),(x+45^{\circ}),$ and $(x+60^{\circ})$. Identify the type of triangle.
Option 1: Obtuse angle triangle
Option 2: Right angle triangle
Option 3: Isosceles triangle
Option 4: Equilateral triangle
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
Correct Answer: Right angle triangle
Solution :
Given: Angles of the triangles is $(x-15^{\circ}),(x+45^{\circ}),$ and $(x+60^{\circ})$.
Let $\angle A =(x-15^{\circ}) $
$\angle B =(x+45^{\circ}) $
$\angle C =(x+60^{\circ}) $
We know that the sum of the angles of a triangle is $180^\circ$.
So, $(x-15^{\circ})+(x+45^{\circ})+(x+60^{\circ}) = 180^{\circ}$
⇒ $3x+90^{\circ}=180^{\circ}$
⇒ $x=30^{\circ}$
Putting the values we get:
$\angle A =(30-15^{\circ})=15^{\circ} $
$\angle B =(30+45^{\circ})=75^{\circ} $
$\angle C =(30+60^{\circ}) =90^{\circ}$
Since one of the angles is $90^{\circ}$,
⇒ The triangle is right-angled.
Hence, the correct answer is the Right angle triangle.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
