Before finding the value of the angle CBD in rhombus ABCD, remember that the sum of the angles of any quadrilateral is 360 °.
Now let’s write ABCD for a given rhombus.
A + B + C + D = 360 °.
Since the opposite angles of the rhombus are equal, we can write A = C, and B = D.
Thus, the above equality can be written in another way.
2A + 2B = 360 °.
Now we substitute the numerical value of the angle A and calculate the value of the angle B.
2 × 56 ° + 2B = 360 °.
112 ° + 2B = 360 °.
2B = 360 ° – 112 °.
2B = 248 °.
B = 248 °: 2.
B = 124 °.
Now let’s write for angle B.
B = ABD + CBD.
Since, according to the rule of the diagonal of a rhombus, its angles are divided in half, the angle ABD is equal to the angle CBD.
Thus, the CBD angle value can be recorded and calculated.
B = 2CBD.
2CBD = 124 °.
CBD = 124 °: 2.
CBD = 62 °.
Answer: CBD = 62 °.
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