In a triangle ABC, C = 90˚, and A = 70˚, CD-bisector. Find the angles ∆BCD.
September 12, 2021 | education
| Since the angle is C = 90 °, the ABC triangle is rectangular. It is known that the angle A = 70 °. One of the properties of a triangle says that the sum of all its angles is 180 °. Based on this, we find the angle B:
B = 180 ° – A – C;
B = 180 ° – 70 ° – 90 °;
B = 180 ° – 160 °;
B = 20 °;
The bisector CD divides the angle C into two equal angles:
ACD = DCB = 1/2 C;
ACD = DCB = 1/2 90 °;
ACD = DCB = 45 °;
CDB = 180 ° – B – DCB;
CDB = 180 ° – 20 ° – DCB;
CDB = 180 ° – 20 ° – 45 °;
CDB = 180 ° – 65 °;
CDB = 115 °.
Answer: The angles in the DCB triangle are 20 °, 45 °, 115 °.
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