Question

In a ∆ABC, if A < B < 45°, then the ABC is a/an
a) acute triangle.
b) right triangle.
c) obtuse triangle.
d) equilateral triangle.
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Answer 1

Given : ∆ABC   ∠A < ∠B < 45°

To Find :  Type of triangle

a) acute triangle.

b) right triangle.

c) obtuse triangle.

d) equilateral triangle.

Solution:

∠A < ∠B < 45°

Add both angles

=> ∠A + ∠B  < 45° + 45°

=> ∠A + ∠B <  90°

Add angle C both sides

=> ∠A + ∠B + ∠C  < 90° + ∠C

Sum of angles of a triangle is 180°

=> 180° < 90° + ∠C

=> 90°  <  ∠C

Hence  ∠C is obtuse angle

so Triangle is obtuse angled triangle

acute triangle. has all angles acute ( less than 90°)

right angle triangle has one angle right angle= 90°

obtuse angled triangle has one obtuse angle greater than 90°

Equilateral triangle has all angles equal to 60°

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Answer 2

Answer:

Option C is the correct answer.