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1 vote
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.

10 ABCD is a trapezium. B 16 cm C х 12.5 cm D A 24.3 cm Work out the size of angle-example-1

2 Answers

10 votes

hmm the answer is 45.cm because

User Ian Chu
by
4.4k points
9 votes

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:


  • \theta = D
  • O = 12.5
  • A = 8.3


\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.

User Nigel Charman
by
5.4k points