Last modified on April 23rd, 2021

chapter outline

 

Acute Angle

What is an Acute Angle

An acute angle is defined as an angle that measures more than 0° and less than 90°. In other words, any angle smaller than a right angle is an acute angle.

Acute Angle

Two or more acute angles can form a right angle (equals 90°) or an obtuse angle (greater than 90°). When the two acute angles make a right angle each measuring 45°, they are called congruent acute angles.

A few more examples of acute angle are shown below:

Examples of Acute Angle

Acute Angles in Real Life

  • All angles in an acute angle triangle, two angles each in obtuse, and right angle triangle
  • Alphabets A, K, M, N, V, W, X, Y, and Z
  • Objects of everyday use such as funnel, coat hanger, hands of wall clock showing 10’ o clock, a partly-open cupboard door, and kitchen tongs
  • Study materials such as a pencil point, opened book, divider, compass, and set squares
  • Geometric shapes such as arrowhead, ‘<‘, and ‘>’ signs
  • A slice of watermelon
  • Branches of a tree
  • Spokes of a bicycle
  • The opened mouth of a crocodile
  • The opened beak of a bird
  • The intersection of a crossroad showing ‘one way’ or ‘no right turn’

Choose from the given options the acute angles.

Solution:

As we know,
Acute angles are angles less than 90°,
Hence, options (a), (b), and (c) are acute angles.

Which of the following options given in the clock timing gives an acute angle?

Solution:

As we know,
Acute angles are angles less than 90°,
Hence, options (b) and (d) are acute angles.

Find x in the given triangle and state whether it is an acute angle triangle

Solution:

As we know,
The sum of the interior angles in a triangle is 180°,
Thus,
In △ABC,
∠ABC + ∠BCA + ∠CAB = 180°, here ∠ABC = 60°, ∠CAB = 60°
60° + ∠BCA + 60° = 180°
∠BCA = 180° – (60° + 60°)
∠BCA = (x°) = 60°
Since all three angles ∠ABC, ∠BCA, ∠CAB measure less than 90°, △ABC is an acute angle triangle

Identify the acute angles in the given polygon ABCDE.

Solution:

As we know,
Sum of the interior angles of a pentagon = 540°
Now,
∠ABC +∠BCD + ∠CDE + ∠DEA +∠EAB = 540°
80° + 158° + ∠CDE + 94° + 132° = 540°
∠CDE = 540° – 464°
∠CDE = (x°) = 76°
Thus, ∠ABC and ∠CDE measure less than 90° and are acute angles.

FAQs

Q1. How many acute angles are found in an acute triangle?

Ans. There are three acute angles in an acute triangle.

Q2. How many acute angles does a right triangle have?

Ans. There are two acute angles in a right triangle.

Q3. How many acute angles are in an obtuse triangle?

Ans. There are two acute angles in an obtuse triangle.

Q4. How many acute angles are in a rhombus?

Ans. Two among the four angles in a rhombus are acute.

Last modified on April 23rd, 2021

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