What is the type of this triangle?

Geometry Level 1

If a triangle has two angles equal and the third angle is double of them. What can you say about this triangle?

Such a triangle is not possible It is an obtuse angled triangle It is an acute angled triangle It is a right angled triangle

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2 solutions

Pham Khanh
Aug 18, 2016

Call the 2 equal angles has a magnitude of a o a^{\text{o}} . So the third angle has the magnitude of 2 a o 2a^{\text{o}} . Also the sum of the interior angles of a triangle is 180 o \text{180}^{\text{o}} . So a o + a o + 2 a o = 180 o a^{\text{o}}+a^{\text{o}}+2a^{\text{o}}=\text{180}^{\text{o}} 4 a o = 180 o \iff 4a^{\text{o}}=\text{180}^{\text{o}} a o = ( 180 4 ) o = 4 5 o \iff a^{\text{o}}=\bigg (\frac{180}{4} \bigg )^{\text{o}}=45^{\text{o}} 2 a o = ( 45 × 2 ) o = 9 0 o \iff 2a^{\text{o}}=(45 \times 2)^{\text{o}}=90^{\text{o}} Cause it has a right angle (the third one) so the answer is I t i s a r i g h t a n g l e d t r i a n g l e \Large \boxed{It~is~a~right~angled~triangle}

Krishna Karthik
Nov 19, 2018

45º,45º,90º

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