Angles, lines and triangles：练习题

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

In the diagram, lines \(PQ\) and \(RS\) are parallel. A transversal line intersects them such that a pair of allied (co-interior) angles are represented by \((4x + 20)^\circ\) and \((x + 10)^\circ\).
Find the value of \(x\).

The interior angles of a triangle are \(x^\circ\), \((x + 20)^\circ\), and \((2x - 40)^\circ\).
Calculate the size of the largest exterior angle of this triangle.

Two straight lines intersect at a point. One of the angles formed by the intersection is \(48^\circ\).
What is the size of the angle vertically opposite to it?

Two parallel lines are intersected by a transversal. A pair of allied (co-interior) angles are represented by \(4x\) and \(x + 20\).
Find the value of \(x\).

State the size of each interior angle in an equilateral triangle.

In triangle \(PQR\), side \(QR\) is extended to a point \(S\). Angle \(PQR = 55^\circ\) and angle \(QPR = x^\circ\).
If the exterior angle \(PRS = 122^\circ\), find the value of \(x\).

In triangle PQR, the side PQ is extended to a point S. Given that \(PQ = PR\) and the exterior angle \(RQS = 130^\circ\), find the size of angle \(QPR\).

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

The diagram shows two triangles, \(ABC\) and \(BCD\).
Triangle \(ABC\) is an equilateral triangle.
Triangle \(BCD\) is an isosceles triangle where \(BC = BD\) and angle \(CBD = 40^\circ\).

(a) Find the size of angle \(ABD\).
(b) Find the size of angle \(BDC\).