Question

A triangle with one obtuse angle and two acute angles is called
(a) Right angled triangle
(b) acute angled triangle
(c) Obtuse angled triangle
(d) None

Answer 1

Hint: First, we have to understand each and every angled triangle meaning i.e. Acute angle triangle means angle less than 90. Obtuse angle triangle means angle greater than 90. Right angled triangle means angle exact at 90. Further, we will come to our what the required answer here.

Complete step by step answer:
Here, we will first understand each and every angled triangle given in options.
(i) Acute angled triangle: It means all the angles formed is less than 90 degree i.e. denoted as $<90{}^{\circ }$ . Example is as shown below:

(ii) Obtuse angled triangle: It means one angle formed which is greater than 90 degree i.e. denoted as $>90{}^{\circ }$ . Rest both the angles are acute angles. Example is shown below.

(iii) Right angled triangle: It means one angle formed at exact 90 degree i.e. perpendicular to line denoted as $=90{}^{\circ }$ . Rest both angles are acute angles.

Now, here we have to find which triangle is formed having one angle $>90{}^{\circ }$ and remaining two angles i.e. $<90{}^{\circ }$ . So, we can see that the acute angled triangle is having all the angles $<90{}^{\circ }$ . So, this is not the correct answer.
Similarly, an obtuse angle triangle is made by one angle $>90{}^{\circ }$ and remaining with $<90{}^{\circ }$ . So, this is our required answer.
Thus, a triangle with one obtuse angle and two acute angles is called an Obtuse angled triangle.
Hence, option (c) is the correct answer.

Note: Remember, an obtuse angle triangle is a triangle with one obtuse angle and two acute angles. Since a triangle’s angle must sum to $180{}^{\circ }$ in Euclidean geometry. So, no Euclidean triangle can have more than one obtuse angle.