From the figure, find the values of \(x\) and \(y\).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 130, 50
Two facts settle the angles: angles on a straight line add up to 180°, and the angles of a triangle add up to 180°. The 100° at A lies between side AB and the line CA drawn on beyond A, so it is an exterior angle; the angle inside the triangle at A is what it leaves on the straight line.
Angle A of the triangle \(=180^{\circ}-100^{\circ}=80^{\circ}\)
\(y=180^{\circ}-80^{\circ}-50^{\circ}=50^{\circ}\) (angles of triangle ABC)
\(x=180^{\circ}-y=180^{\circ}-50^{\circ}=130^{\circ}\) (\(x\) and \(y\) lie on the straight line BC)
