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maw
2 months ago
7

If m□ebd=4x-8 and m□ebc=5x+20,find the value of x and m□ebc

Mathematics
1 answer:
AnnZ [12.3K]2 months ago
5 0

Let m□ebd=4x-8 and m□ebc=5x+20

This can be solved only if eb serves as the initial side while bd and bc are positioned opposite each other along a line; hence, c, b, d are in a straight line.

The angles ∠ebd and ∠ebc will create a linear pair. A linear pair signifies that the angles formed on one side of a straight line through a common vertex and are adjacent measure 180°.

That is,

∠ebd + ∠ebc = 180°

4x - 8 + 5x + 20 = 180°

By summing like terms

⇒ 9x + 12 = 180°

⇒ 9x = 180° - 12

⇒ 9x = 168°

⇒ x = (168/9)° = (56/3)°

Now, m□ebc = 5x + 20

= 5 × 56/3 + 20

= 280/3 + 20

= 340/3

Therefore, the solution set is x = (56/3)° and m□ebc = (340/3)°

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