Angles, triangles and polygons：练习题

In a regular polygon, the sum of all interior angles is \(1440^\circ\). Calculate the size of each exterior angle of this polygon.

In a convex quadrilateral ABCD, the interior angles ∠A, ∠B, ∠C, and ∠D are in the ratio \( 2 : 3 : 4 : 6 \). Calculate the magnitude of the largest interior angle.

In a regular \(n\)-sided polygon, each interior angle is \(157.5^\circ\). Find the value of \(n\).

Calculate the size of each exterior angle of a regular decagon (10-sided polygon).

A regular polygon has an interior angle that is \( 4 \) times the size of its exterior angle. How many sides does this polygon have?

Calculate the size of each interior angle of a regular octagon.

The interior angles of a pentagon are \( x^\circ \), \( 2x^\circ \), \( (x+40)^\circ \), \( (x+70)^\circ \) and \( 110^\circ \). Calculate the value of \( x \) and determine the largest exterior angle of this pentagon.

In a convex polygon, the sum of the interior angles is \( 1440^\circ \).
(a) Find the number of sides of this polygon.
(b) Given that the polygon is regular, calculate the size of each exterior angle.
(c) A second regular polygon has an exterior angle that is half the size of the exterior angle found in part (b). Calculate the sum of the interior angles of this second polygon.