In diamond ABCD, the CDA angle is 94 degrees. Find the ACD angle.

It is known:

ABCD – rhombus;

Angle CDA = 94 °;

Find the ACD angle.

1) AC – diagonal, divides the BCD angle in half.

Hence, the angle CDA = 1/2 * angle ВСD.

2) Consider a triangle ACD.

The 2 sides of the triangle are equal, that is, CD = AD.

Hence, angle ACD = angle DAC;

3) The sum of all the angles of the triangle is 180 °.

ACD angle + DAC angle = 180 ° – CDA angle = 180 ° – 94 ° = 180 ° – 90 ° – 4 ° = 90 ° – 4 ° = 86 °;

Then:

ACD angle + DAC angle = 86 °;

2 * angle ACD = 86 °;

Angle ACD = 86 ° / 2;

Angle ACD = 80 ° / 2 + 6 ° / 2;

Angle ACD = 40 ° + 3 °;

Angle ACD = 43 °.