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neonofarm [45]
3 years ago
8

In parallelogram ABCD below, line AC is a diagonal, the measure of angle ABC is 40 degrees, and the measure of angle ACD is 57 d

egrees. What is the measure of angle CAD

Mathematics
1 answer:
Lorico [155]3 years ago
6 0

Answer:

The measure of angle CAD is 83 degrees.

Step-by-step explanation:

Given information: ABCD is a parallelogram, AC is a diagonal, \angle ABC=40^{\circ} and  \angle ACD=57^{\circ}.

The opposite sides of parallelogram are congruent.

The diagonal AC divides the parallelogram in two congruent triangles.

In triangle ABC and ADC,

AB\cong CD                                     (Opposite sides of parallelogram)

\angle ABC\cong \angle ADC         (Opposite angles of parallelogram)

BC\cong DA                                     (Opposite sides of parallelogram)

By SAS postulate,

\triangle ABC\cong \triangle CDA

Since we know that opposite angles of parallelogram are equal, therefore

\angle ABC\cong \angle ADC

\angle ADC=40^{\circ}

According to the angle sum property the sum of interior angles of a triangle is 180 degrees.

\angle CAD+\angle ACD+\angle ADC=180^{\circ}

\angle CAD+57^{\circ}+40^{\circ}=180^{\circ}

\angle CAD=83^{\circ}

Therefore the measure of angle CAD is 83 degrees.

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