In the ABCD parallelogram, the diagonal of the AC with the sides AB and BC

| February 1, 2021 | education

In the ABCD parallelogram, the diagonal of the AC with the sides AB and BC forms angles equal to 45 degrees and 25 degrees, respectively. What is the value of the angle C.

Consider the ABС triangle, in which two angles are known that are formed by the AC diagonal with the sides of the parallelogram, and based on this we find the unknown angle of the parallelogram <ABС = 180 – (<ABС + <BAСS = 180 – (45 + 25) = 180 – 70) = 110 (degrees).

In the task, you need to find the value of the angle C = <BСD = <BAD = 180 – <ABС = 180 – 110 = 70 (degrees).
Here we used such a property of the corresponding angles at parallel straight lines that the sum of the corresponding angles is equal to 180 degrees.

There is a second solution: <C = <BСA = <BСA + <AСD = <BСA + <dietary supplement = 25 + 45 = 70 (degrees).

<BAD = <AСD, as internal criss-crossing angles with parallel straight lines AB and СD.



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