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ABCD diagonals intersect at E. If m∠BAC=4x+5 and m∠CAD=5x-14, then find m∠CAD.

User Dobby
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Answer: m∠CAD = 81°

Explanation: Diagonal is a line that unites opposite sides.

ABCD is a prallelogram. One property of diagonal in a parallelogram is it separates the parallelogram in 2 congruent triangles.

The figure below shows ABCD with its diagonals.

Since diagonal divides a parallelogram in 2 congruent triangles, it means the internal angles are also congruent. So

m∠BAC = m∠CAD

4x + 5 = 5x - 14

x = 19

Then, m∠CAD is

m∠CAD = 5(19) - 14

m∠CAD = 81

The angle m∠CAD is 81°.

ABCD diagonals intersect at E. If m∠BAC=4x+5 and m∠CAD=5x-14, then find m∠CAD.-example-1
User Ramiz Uddin
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