10 ABCD is a trapezium. B 16 cm C х 12.5 cm D A 24.3 cm Work out the size of angle x. Give your answer correct to 1 decimal place.

Question

asked Mar 10, 2023 189k views

2 Answers

Nigel Charman · Answer 1 · 2023-03-15T13:29:20+0000

Answer:

x = 123.6°

Explanation:

Subdivide the trapezium into a rectangle and triangle.

The triangle is a right triangle with hypotenuse CD and height 12.5cm.

The base of the triangle is 24.3 - 16 = 8.3 cm

To find angle D, use the tan trig ratio:

$tan(\theta)=(O)/(A)$ where
$\theta$ is the angle, O is the side opposite the angle A is the side adjacent the angle.

Therefore, for the right triangle:

$\tan(\theta)=(12.5)/(8.3) \implies \theta=56.41583952... \textdegree$

In a quadrilateral, the sum of the angles between the parallel lines is 180°. Therefore, m∠C + m∠D = 180°

⇒ x + 56.41573952... = 180

⇒ x = 180 - 56.41573952...

⇒ x = 123.6° (1 dp)

Alternatively, calculate angle C of the right triangle and add it to 90° to find x.