Find a+ b

Geometry Level 2

In the figure above, A B = A C = B E = B D AB=AC=BE=BD and B C = D E BC=DE . Given that ∠ E B D = 3 8 ∘ \angle EBD=38^\circ , find a + b a+b .


The answer is 109.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Since BE=BD it follows that angle BDE = angle BED = 71. Because the given equal sides it follows that BCF is also 71 degrees and thus BFC = 71 degrees too. Now a + b = 180 - 71 = 109.

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