Can anyone help please

Mathematics

1 answer:

Akimi4 [234]3 years ago

8 0

Answer: X = 27

Step-by-step explanation: If we observe very closely, we have two similar triangles in the diagram. The first one is ABC and the other triangle is EDC. Also take note that angle ACB in the first triangle is equal in measurement to angle ECD (45 degrees) in the other triangle, (Opposite angles).

Hence in triangle ECD, we have identified two angles so far which are angle 2x + 10 and angle 45. Same applies to triangle ABC, we already have two angles which are, 3x - 10 and 45.

However angle D in the second triangle is equal in measurement to angle B in the first triangle

(Alternate angles).

Hence we have a third angle in triangle ABC which is

Angle B = 2x + 10.

Therefore 3x - 10 + (2x + 10) + 45 = 180

(Sum of angles in a triangle)

3x - 10 + 2x + 10 + 45 = 180

By collecting like terms we now have

3x + 2x = 180 + 10 - 10 - 45

5x = 135

Divide both sides by 5,

x = 27

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