Page 166 - Start Up Mathematics_7

Pair Activity

Objective: To verify exterior angle property of a triangle

Step 1: Draw two triangles of exactly the same size and
shape, one on a sheet of glazed paper and other A
on a white drawing sheet. Cut the triangle drawn
on the glazed paper.

Step 2: Mark the three angles of the triangle drawn on B C D
the white sheet. Produce one of its side, say BC
to D as shown in the adjacent figure.
∠ACD is called the exterior angle of ∆ ABC A

formed at vertex C.

Step 3: Now cut out ∠A and ∠B (interior opposite angles
of ∠ACD) from the triangle that is cut from the B
glazed paper. C

A
Step 4: Rearrange the cut outs of ∠A and ∠B on angle
ACD drawn on the white sheet. We find that these
two angles cover ∠ACD entirely and exactly. A B

Hence, we conclude ∠ACD = ∠A + ∠B. B C D

Example 4: Find the value of the unknown exterior angle x in the following figures:

50°
x
30°
x
70°
80°
x 60°
60°
(a) (b) (c)

Solution: We know that exterior angle of a triangle is equal to the sum of its two interior
opposite angles. Therefore,
(a) x = 60° + 70° = 130° (b) x = 30° + 60° = 90°

(c) x = 80° – 50° = 30° ( Unknown interior angle = Exterior angle – known
interior angle)

Sum of Three Angles of a Triangle

There is a remarkable property connecting the three angles of a triangle. Let’s learn it through the
following activity.

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