Intermediate Mathematics

Angles

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Angles

Angle - An angle is formed by two rays with a common endpoint. Angles are measured in degrees (°).
Straight Angle = 180°
Right angle = 90°
Acute Angle > 0° and < 90°
Obtuse Angle > 90° and < 180°

Angle ABC is a straight angle.
Angles ABD and DBC are right angles.
Angles CBE and DBE are acute angles.
Angle ABE is an obtuse angle.

Angles

The sum of the three angles in any triangle is always 180°.

a + b + c = 180°

Knowing that the sum of the angles of triangle is 180° can help you to solve problems about triangles.

Angles

In this triangle, angle b is a right angle and angle c = 40°. What is the measure of angle a?

a + b + c = 180°

Since b is a right angle, b	= 90°.
The problem states that c	= 40°.
Therefore, a + 90° + 40°	= 180°
a + 130°	= 180°
a + 130° − 130°	= 180° − 130°
a	= 50°

Angle a measures 50°.

Angles

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An obtuse angle

Question 1 of 8

This is an acute angle. It measures less than 90°. Try again

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°.

One of these figures is an obtuse angle. Try again.

An obtuse angle is larger then a right angle and smaller then a straight angle.

Angles

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An acute angle

Question 2 of 8

This is an acute angle. It measures less than 90°.

This is a right angle. The square in the corner shows that it measures 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is obtuse. It is greater than 90° and less than 180°. Try again.

One of these figures is an acute angle. Try again.

An acute angle is smaller then a right angle.

Angles

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A right angle

Question 3 of 8

This is an acute angle. It measures less than 90°. Try again

This is a straight angle. It measures 180°. Try again.

This angle is an obtuse angle. It measures more than 90° and less than 180°. Try again.

This is an acute angle. It measures less than 90°. Try again.

A right angle looks like a square corner and measures 90°.

A right angle measures 90°.

Angles

There are five question remaining. In each of these question, you will be asked to find the size of a missing angle.

Angles

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Angle ABC is a right angle. If angle n is 40°, how large is angle m?

Question 4 of 8

90° − 40° = 50°
Angle m is 50°.

Angle ABC is 90° , and angle m is only part of this right angle. It is less than 90°. Try again.

Angle ABC is 90°, and angle m is only part of this right angle. Try again.

Angle m and n together from a 90° angle. Subtract 40° from 90° .Try again.

One of these is size of angle m. Try again.

Since angle ABC is a straight angle, angle m + angle n = 90°.

Angles

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If angle VST is 45° , how large is angle RSV?

Question 5 of 8

Angle RST is a straight angle, or 180° , not a right angle. Subtract 45° from 180° to find angle RSV. Try again.

Subtracting 45° from 180° does not give 155° for angle RSV. Try again.

180° − 45° = 135°
Angle RSV is 135°.

Angle RST is a straight angle, or 180°. Subtract 45° from 180° to find angle RSV. Try again.

One of these is size of angle RSV. Try again.

Since angle RST is a straight angle, angle RSV + angle VST = 180°.

Angles

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Angle f is 50° and angle g is 60°. How large is angle h?

Question 6 of 8

50° + 60° = 110° and 180° − 110° = 70°
Angle h is 70°.

110° is the sum of angles f and g. Subtract this from 180° to find angle h. Try again.

Angle ABC is a straight angle, or 180°. Angle f, g, and h together must add to 180°. Try again.

One of these is size of angle h. Try again.

Since angle ABC is a straight angle, angle f + angle g + angle h = 180°.

Angles

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Angle SRT = 90° and angle RST = 30°. How large is angle RTS?

Question 7 of 8

The three angles of triangle have a sum of 180°. Subtract the sum of angles SRT and RST from 180°. Try again

90° + 30° = 120° and 180° − 120° = 60°
Angle RTS is 60°.

The three angles of triangle have a sum of 180°. Subtract the sum of angles SRT and RST from 180°. Try again

120° is the sum of angles SRT and RST. Subtract this from 180° to find angle RTS. Try again.

One of these is size of angle RTS. Try again.

The three angles of a triangle have a sum of 180°.

Angles

Click on the correct answer.

Angle GFH = 40° and angle GHF = 40°. How large is angle FGH?

Question 8 of 8

40° − 40° = 80° and 180° − 80° = 100°
Angle FGH is 100°.

The three angles of triangle have a sum of 180°. Subtract the sum of angles GFH and GHF from 180°. Try again

80° is the sum of angles GFH and GHF. Subtract this from 180° to find angle FGH. Try again.

The three angles of triangle have a sum of 180°. Subtract the sum of angles GFH and GHF from 180°. Try again.

One of these is size of angle FGH. Try again.

The three angles of a triangle have a sum of 180°.

Angles