Question 1192517: In concave quadrilateral ABCD, the angle at A measures 44°. △ABD is isosceles,
BC bisects ∠ABD,
and DC bisects ∠ADB.
What are the measures (in degrees) of
∠ABC, ∠ADC, and ∠1?
we have an ISOSCELES TRIANGLE, but we are given the VERTEX ANGLE (which is ANGLE A and it equals 44 degrees). Now again, we need to begin with is equation BASE ANGLE + VERTEX ANGLE+ SECOND BASE ANGLE = 180. If you make both base angles a variable ... and the vertex angle 80 .... you will find the value of 'x' ... which is a base angle. Now, once you obtain the BASE ANGLE ... you need to "BISECT" these base angles ... because this will give you the measure of angle ABC and ADC ...
Then you need to take the "small" triangle inside the bigger triangle (ABD) ... you again use the equation BASE ANGLE + VERTEX ANGLE+ SECOND BASE ANGLE = 180, but the base angles will be your answer for BISECTED angles ... which, in turn, will give you angle 1
Answer by ikleyn(52786)   (Show Source):
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