Page 168 - Start Up Mathematics_7

Solution: (a) 65° + y = 130° (Exterior angle property)

⇒ y = 65°
Also, 130° + x = 180° (Linear pair)
⇒ x = 50°

(b) 50° + 60° + y = 180° (Angle sum property)
⇒ y = 70°
Also, x + y = 180° (Linear pair)

⇒ x + 70° = 180°
⇒ x = 110°
(c) ∠BCA = x = y (Vertically opposite angles)

∠ABC = y (Vertically opposite angles)
∠BAC = y (Vertically opposite angles)
Now, y + y + y = 180° (Angle sum property)

⇒ 3y = 180° ⇒ y = 60°
⇒ x = y = 60°
Example 7: Can you have a triangle with two obtuse angles?
Solution: Since the sum of three angles of a triangle cannot exceed 180°, therefore, such a
triangle is not possible.

Example 8: Can you have a triangle with all the three angles less than 60º?
Solution: Such a triangle is not possible as the sum of the angles cannot be less than 180°.

• In an equilateral triangle each angle measures 60º.
• In an isosceles triangle the angles opposite equal sides are equal.
• In a scalene triangle no two angles are equal.

Example 9: Find the value of angle x in each of the following figure:

120°
x

100° 25°
x
55°
x x
(a) (b) (c) (d)
Solution: (a) x = 55° (Angles opposite equal sides of an isosceles triangle)
(b) The third angle of the triangle is also x as it is an isosceles triangle.

100° + x + x = 180° (Angle sum property)
⇒ 2x = 180° – 100° ⇒ 2x = 80° ⇒ x = 40° 120°
(c) Since it is an isosceles triangle, the other base angle is also x.

x + x = 120° (Exterior angle property)
⇒ 2x = 120° ⇒ x = 60° x x

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