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Every triangle has at least _______ acute angle (s). Fill in the blanks to make the statement true.

Solution:

Given, every triangle has at least _______ acute angle (s).

We have to fill in the blanks to make the statement true.

An acute angle is a type of angle that measures less than 90° i.e. measure between 0° to 90°.

We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.

Let the angle be a, b and c

(i) consider if one angle a = 90°,

90° + b + c = 180°

b + c = 180° - 90°

b + c = 90°

Since the sum of angles is 90 degrees, the angles b and c must be less than 90 degrees.

(ii) consider if one angle a = 100°

100° + b + c = 180°

b + c = 180° - 100°

b + c = 80°

Since the sum of angles is 80 degrees, the angles b and c must be less than 90 degrees.

(iii) consider if one angle a = 50°

50° + b + c = 180°

b + c = 180° - 50°

b + c = 130°

Since the sum of angles is 130 degrees, the angles b and c may be a right angle or obtuse angle (greater than 90°) or both can be acute angles.

Therefore, the triangle has two acute angles.

✦ Try This: Every triangle has at least _______ obtuse angle (s). Fill in the blanks to make the statement true.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 58

Summary:

Every triangle has at least two acute angles.

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