In triangle ABC, angle C = 31, AD is the bisector of angle A, angle ADB is 56. Find angle B.
| March 26, 2021 | education
The sum of adjacent angles is 180 °, which means:
∠ АDС = 180 ° – ∠ АDВ = 180 ° – 56 ° = 124 °;
The sum of all angles in a triangle is also 180 °, so:
∠ CAD = 180 ° – ∠ С – ∠ АDC = 180 ° – 31 ° – 124 ° = 180 ° – 155 ° = 25 °;
∠ BAD = ∠ CAD = 25 °;
∠ B = 180 ° – ∠ BAD – ∠ ADB = 180 ° – 25 ° – 56 ° = 180 ° – 81 ° = 99 °.
Answer: 99 °
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