Geometrical terms：練習問題

A solid 3D shape has exactly one circular base and one vertex. What is the name of this geometrical term?

Which of the following geometric properties is not always true for a rhombus?

A regular polygon has an interior angle of \( 162^\circ \). How many sides does this polygon have?

Which of the following polygons is defined as having exactly ten sides?

Point \( X \) is at a bearing of \( 125^\circ \) from point \( Y \). Calculate the three-figure bearing of point \( Y \) from point \( X \).

Lines PQ and RS are parallel. A transversal T intersects PQ at A and RS at B. If the interior angle \( \angle QAB = 118^\circ \), calculate the reflex angle formed by \( \angle SAB \).

ABCDE is a regular pentagon. A line segment CF is drawn parallel to the side AB, where C, E, D are vertices in order. Calculate the size of angle ECF.

In the diagram, three points are located such that point \( B \) is a vertex of a right-angled triangle \( ABC \). The line segment \( AB \) is perpendicular to the line segment \( BC \).

(a) State the size of angle \( ABC \) in degrees.
(b) Identify whether angle \( ABC \) is an acute, obtuse, or right angle.
(c) If a third line segment \( AC \) is drawn to form triangle \( ABC \), and the lengths of sides \( AB \) and \( BC \) are not equal, state the specific geometrical term for this type of triangle based on its side lengths.

In the diagram, the line segment \( PQ \) is a straight line. Point \( R \) lies on the line such that an angle is formed by a ray \( RS \).

(a) If angle \( PRS = 5x + 15^{\circ} \) and angle \( QRS = x + 45^{\circ} \), find the value of \( x \) using the property of angles on a straight line.
(b) Using your answer from part (a), calculate the size of angle \( PRS \).
(c) State whether angle \( QRS \) is an acute, obtuse, or reflex angle.