We know that the sum of the interior angles of a triangle equals 180, then,in this case we have the following equation:
then, solving for b, we get:
now that we have that b = 41, we can find the measure of each angle:
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1 answer:
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Answer:
46
Step-by-step explanation:
∠DAC ≅ ∠ACB because they are opposite interior angles where transversal AC crosses parallel lines BC and AD.
∠DAC ≅ ∠CAB because they are corresponding angles of the similar triangles ΔABC and ΔACD.
Hence ∠ACB ≅ ∠CAB and ΔABC is isosceles with side lengths both being 9. The corresponding side lengths of ΔACD are 12, meaning the base of ΔABC, segment AC, is 12. The scale factor of ΔACD to ΔABC is then 12:9 = 4:3, so the base AD of ΔACD is (4/3)×12 = 16.
So, the side lengths of the trapezoid are ...
- AB = 9
- BC = 9
- CD = 12
- DA = 16
and the perimeter is 9 +9 +12 +16 = 46 units.
