Angles: Practice Questions

Which of the following terms describes an angle that is greater than \(180^\circ\) but less than \(360^\circ\)?

Points \(A\), \(B\), and \(C\) lie on a straight line. A line segment \(BD\) is drawn such that angle \(\angle ABD = 124^\circ\). What is the size of the reflex angle \(\angle CBD\)?

In a pentagon, four of the interior angles are \(100^\circ\), \(110^\circ\), \(120^\circ\), and \(95^\circ\). Calculate the size of the exterior angle at the fifth vertex.

Two parallel lines are intersected by a transversal line. If one of the angles formed is \(72^\circ\), which of the following must be the size of its corresponding angle?

In a right-angled triangle, one of the acute angles is \(34^{\circ}\). Calculate the size of the other acute angle.

Points A, B, and C lie on a straight line. A ray BD is drawn such that it creates two adjacent angles on the line. Angle ABD is given as \( (4x + 10)^\circ \) and angle CBD is given as \( (2x + 20)^\circ \).
(a) Write down an equation involving \( x \) using the properties of angles on a straight line.
(b) Solve the equation to find the value of \( x \).
(c) Calculate the actual size of angle ABD.