Page 167 - Start Up Mathematics_7

Pair Activity

Objective: To verify angle sum property of a triangle
B
Step 1: Draw and cut two triangles of exactly the same size 2
and shape from a sheet of glazed paper.

Step 2: Mark the three angles of the triangle. Paste one of
the triangles on a white chart as shown.
Step 3: Cut out ∠A, ∠B and ∠C from the triangular A 1 3 C

lamina that is not pasted. Rearrange the cut outs Fig. 1
of ∠A, ∠B and ∠C as to form adjacent angles
with no overlapping. Ensure the three vertices
A, B and C meet at a point as shown in Fig. 2.
The three angles lie along a straight line. Since the

sum of the adjacent angles along a line add up to 2
180º, therefore we conclude the sum of three angles 1 3
of a triangle is 180º, i.e., ∠A + ∠B + ∠C = 180°. Fig. 2

Example 5: Find the value of the unknown x in the following figures:

x 40°
70° 3x
(a) (b) (c) (d)

x 60° x x x x 2x

Solution: We know that the sum of three angles of a triangle is 180°. Therefore,

(a) x + 70° + 60° = 180° ⇒ x = 50°
(b) x + x + x = 180° ⇒ x = 60°

(c) 40° + x + x = 180° ⇒ 2x = 180° – 40° ⇒ x = 70°

(d) 3x + 2x + 90° = 180° ⇒ 5x = 90° ⇒ x = 18°

Example 6: Find the values of the unknown x and y in the following figures:

y
A
A
A
50°
(a) 65° (b) (c)
130°
x y x B x C
B C y 60° y y
B C

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