Question

Also find the measure of BEF as well

Answer 1

∠ABC = 84°

∠BEF = 64°

Explanation:

∠ABC is supplementary to the 96° angle shown, so is 180° -96° = 84°.

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∠ABD, marked as (x+y)°, is a vertical angle with ∠EBC, so has the same measure, 96°. ∠BEF, marked as y°, is a vertical angle with the one marked 2x°.

These relationships can be expressed as two equations:

• x + y = 96
• 2x = y

Using the second of these equations to substitute for y in the first equation, we have ...

x + 2x = 96

x = 96/3 = 32

y = 2x = 2·32 = 64 . . . . . . substitute the value of x into the second equation

Then ∠BEF = 64°.