Angle EBC=3r+10 Angle ABE=2r-20 Find angle EBF

Mathematics

1 answer:

tester [12.3K]2 months ago

7 0

Solution:

Angles EBC and ABE are adjacent and form a straight line.

Therefore, ∠EBC plus ∠ABE equals 180 degrees.

Expressed as: 3r + 10 plus 2r - 20 equals 180.

Simplifying gives 5r minus 10 equals 180.

Adding 10 to both sides, 5r equals 190.

Dividing both sides by 5 results in r equals 38.

Next, substitute the value of r.

Given that ∠EBF equals ∠ABE,

∠EBF equals 2r minus 20.

Plugging in r = 38: ∠EBF = 2 × 38 minus 20.

Which simplifies to 76 minus 20,

Hence, ∠EBF is 56 degrees (Final answer).

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