Maharashtra Board Class 7 Maths part 1 Chapter 4 Angles and Pairs of Angles PDF Download

Angles and Pairs of Angles

Let's Recall

Write the name of the angle shown alongside.

Write the name of its vertex.

Write the names of its arms.

Write the names of the points marked on its arms.

The Interior and Exterior of an Angle

In the plane of the figure alongside, the group of points like point N, point M, point T which are not on the arms of the angle, form the interior of the angle PQR.

The group of points in the plane of the angle like point G, point D, point E, which are neither on the arms of the angle nor in its interior, form the exterior of the angle.

Teacher's Note

In your classroom, you can show students a triangle drawn on paper. Point the interior (inside the triangle), exterior (outside), and arms (the sides). Like a room - inside is interior, outside is exterior, walls are the arms.

Exam Trick

Remember: Interior = inside. Exterior = outside. These two words sound similar to "in" and "ex" which mean inside and outside.

Points to Remember

An angle has one vertex point where two arms meet.
The interior is the space inside the angle.
The exterior is the space outside the angle.
Points on the arms are on the angle itself.

Adjacent Angles

Look at the angles in the figure alongside. The ray MQ is a common arm of the angles BM Q and QMD while M is their common vertex. The interiors of these angles do not have a single common point. They may be said to be neighbouring angles. Such angles are called adjacent angles.

Adjacent angles have one common arm and the other arms lie on opposite sides of the common arm. They have a common vertex. Adjacent angles have separate interiors.

In the given figure, MB is the common arm of the angles BMD and BMQ. However, they are not adjacent angles because they do not have separate interiors.

Teacher's Note

Show students two books standing next to each other on a desk. They share one edge (common arm) and are next to each other (adjacent). This is like adjacent angles in geometry.

Exam Trick

Adjacent = next to each other. Think "ad-join" = join together. Two angles that join at one arm are adjacent angles.

Points to Remember

Adjacent angles must have one common arm.
The other arms must be on opposite sides of the common arm.
They must have the same vertex point.
The interiors must not overlap or be the same.

Now I Know!

Two angles which have a common vertex, a common arm and separate interiors are said to be adjacent angles.

Complementary Angles

Draw angle PQR, a right angle.

Take any point S in its interior.

Draw ray QS.

Add the measures of the angles PQS and SQR. What will be the sum of their measures?

If the sum of the measures of two angles is 90° they are known as complementary angles.

Here, angle PQS and angle SQR are mutually complementary angles.

Teacher's Note

In your classroom, show a right angle (90°) with your arms. Now bend one arm to divide it into two smaller angles. Their sum is still 90°. This is like a corner of a square that gets divided into two smaller corners.

Exam Trick

Complementary = 90°. Remember: "Complete" a right angle = 90°. If one angle is 30°, the other must be 60° (30° + 60° = 90°).

Points to Remember

Complementary angles add up to exactly 90 degrees.
They can be adjacent or not adjacent.
If one angle is known, subtract it from 90° to get the other.
Right angles are made of two complementary angles.

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