SOLUTION: ABCD is rhombus. If ∠BAC = 40°, find ∠ADB and ∠ ABC.

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Question 1164931: ABCD is rhombus. If ∠BAC = 40°, find ∠ADB and ∠ ABC.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


In a rhombus, just like any other parallelogram, the angles opposite each other are equal in measure and the angles adjacent are supplementary.


John

My calculator said it, I believe it, that settles it
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
I won't do your for you.  I'll do one exactly like it.
ABCD is rhombus. If ∠BAC = 36°, find ∠ADB and ∠ ABC.


∠ DAC = 36°   because the diagonals of a rhombus bisect each other.
AC ⊥ BC       because the diagonals of a rhombus are perpendicular.
ΔAED is a right triangle because two sides are perpendicular.
∠ ADB = 54°   because the two angles of a right triangle are complementary.

AB ≅ AD       Sides of a rhombus are congruent
ΔABD is isosceles   2 sides congruent
∠ ABD = 54°   Base angles of isosceles triangle are congruent
AB ≅ BC       Sides of a rhombus are congruent
ΔABC is isosceles   2 sides congruent
∠ BCA = 36°   Base angles of isosceles triangle are congruent
∠BAC + ∠BCA + ∠ABC = 180°    Property of all triangles
∠ABC = 180° - ∠BAC - ∠BCA  
∠ABC = 180° - 36° - 36° = 108°

Now do yours the same way.

Edwin
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