**Angles and their measures worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on angles, their measures and their classifications.

**Problem 1 :**

Name the angles in the figure given below.

**Problem 2 : **

Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°.

Find the angle of vision seen by the left eye alone.

**Problem 3 :**

Plot the points L (-4, 2), M(-1, -1), N (2, 2), Q(4, -1) and P(2, -4). Then, measure and classify the following angles as acute, right, obtuse or straight.

(i) m∠LMN

(ii) m∠LMP

(iii) m∠NMQ

(iv) m∠LMQ

**Problem 4 :**

Use a protractor to draw two adjacent acute angles ∠RSP and ∠PST so that ∠RST is

(a) Acute

(b) Obtuse

**Problem 1 :**

Name the angles in the figure given below.

**Solution :**

There are three different angles.

∠PQS or ∠SQP

∠SQR or ∠RQS

∠PQR or ∠RQP

We should name any of the angles as ∠Q, because all three angles have Q as their vertex. The name ∠Q would not distinguish one angle from others.

**Problem 2 :**

Each eye of a horse wearing blinkers has an angle of vision that measures 100°. The angle of vision that is seen by both eyes measures 60°.

Find the angle of vision seen by the left eye alone.

**Solution : **

We can use the angle addition postulate.

m∠2 + m∠3 = 100° (The total for left eye is 100°)

m∠3 = 100° - m∠2 (Subtract m∠2 from each side)

m∠3 = 100° - 60° (Substitute 60° for m∠2)

m∠3 = 40° (Subtract)

Hence, the vision for the left eye alone measures is 40°.

**Problem 3 :**

Plot the points L (-4, 2), M(-1, -1), N (2, 2), Q(4, -1) and P(2, -4). Then, measure and classify the following angles as acute, right, obtuse or straight.

(i) m∠LMN

(ii) m∠LMP

(iii) m∠NMQ

(iv) m∠LMQ

**Solution : **

Plot the given points in xy coordinate plane.

We can use the protractor to measure and classify each angle as shown below.

MEASURE (i) m∠LMN = 90° (ii) m∠LMP = 180° (iii) m∠NMQ = 45° (iv) m∠LMQ = 135° |
CLASSIFICATION Right angle Straight angle Acute angle Obtuse angle |

**Note : **

Two angles are adjacent angles, if they share a common vertex and side, but have no common interior points.

**Problem 4 :**

Use a protractor to draw two adjacent acute angles ∠RSP and ∠PST so that ∠RST is

(a) Acute

(b) Obtuse

**Solution :**

**Solution (a) :**

**Solution (b) :**

After having gone through the stuff given above, we hope that the students would have understood "Angles and their measures worksheet".

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