Answer:
x = 123.6°
Step-by-step 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:
[tex]tan(\theta)=\dfrac{O}{A}[/tex] where [tex]\theta[/tex] is the angle, O is the side opposite the angle A is the side adjacent the angle.
Therefore, for the right triangle:
- [tex]\theta[/tex] = D
- O = 12.5
- A = 8.3
[tex]\tan(\theta)=\dfrac{12.5}{8.3} \implies \theta=56.41583952... \textdegree[/tex]
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.
