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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 125 Cm D A 243 Cm Work Out The Size Of Angle X Give Your Answer Correct To 1 Decimal Place class=

Sagot :

hmm the answer is 45.cm because

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.

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