Find the measure of the unknown angle

Geometry Level 1

In triangle A B C ABC shown above, A D = D F AD=DF and D E = E F DE=EF . Find the measure of the unknown, pink angle (in degrees).

75 120 60 90 100

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Consider the diagram on the left.

x + 2 x + 45 + 60 = 180 x+2x+45+60=180

3 x + 105 = 180 3x+105=180

3 x = 75 3x=75

x = 25 x=25

Finally the unknown angle is 4 x = 4 ( 25 ) = 4x=4(25)= 10 0 ∘ \boxed{100^\circ}

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I need a bit of help pls?

monster muri - 7 months, 1 week ago
Trevor Belmont
Mar 11, 2020

75=3x x=25 25×4=100

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