i) In the figure
the angles are 70°, x°, x° (angles in an Isosceles triangle)
Also 70° + x° + x° = 180° (angle – sum property)
2x° + 70°= 180°
2x° = 180° – 70° [∵ y° = x°]
2x° = 110°
x°= 110°/2 = 55°
ii) From the figure,
the Interior opposite angles of x are 50°, 500 (angles in an isosceles triangle)
50° + 50° = x° (exterior angle is equal to sum of the Interior opposite angles)
∴ x = 100°
iii) From the figure,
y° = 30° (vertically opposite angles)
Also y = x° – 30° (equal angles of an Isosceles triangles)
∴ x° = 30° and y = 30°
iv) From the figure,
a + 110° = 180° (linear pair of angles)
∴ a = 180° – 110°= 70
Also y° = a° = 70° (equal angles of an isosceles triangle)
x + y + a = 180 (sum of interior angles)
x + 70 + 70 = 180
x + 140 = 180
x = 180 – 40 = 40°,
∴ x = 40°
