Question

DCB is a straight line. Find the unknowns in the following figure.

Answer 1

`\sf\\(i)\ \angle ABC=\angle BAC\ \ \ [\textsf{Base angles of isosceles triangle are equal.}]\\or,\ x=y\\\\(ii)\ \angle ABC+\angle BAC=\angle ACD\ \ \ [\textsf{An exterior angle of a triangle is equal to the sum}\\\textsf{ }\textsf{ }\textsf{ }\ \textsf{ of the opposite interior angles.]}\\or,\ x+y=150^o\\or,\ x+x=150^o\\or,\ 2x=150^o\\or,\ x=75^o=y`

Alternative method:

`\sf\\(i)\ \angle ACD+\angle ACB=180^o\ \ \ [\textsf{Sum of angles in straight line is 180}^o.]\\or,\ 150^o+\angle ACB=180^o\\or,\ \angle ACB=30^o\\\\(ii)\ \angle ABC=\angle BAC\ \ \ [\textsf{Base angles of isosceles triangle are equal.}]\\or,\ x=y\\`

`\sf\\(iii)\ \angle ABC+\angle BAC+\angle ACB=180^o\ \ \ [\textsf{Sum of angles of triangle is }180^o.]\\or,\ y+x+30^o=180^o\\or,\ x+x+30^o=180^o\\or,\ 2x=150^o\\or,\ x=75^o=y`

Answer 2

Angle ACB measures 30°.

x = y since the base angles of an isosceles triangle are congruent.

30 + 2x = 180

2x = 150

x = y = 75°