In triangle BDE, angle B is 30% of angle D, and angle E is 19 degrees greater than angle D. Find angle B.
March 31, 2021
Given the condition:
angle E = angle D + 19;
angle B = 0.3 * angle D.
By the theorem on the sum of the angles of a triangle:
angle B + angle D + angle E = 180 degrees;
0.3 * angle D + angle D + angle D + 19 = 180;
2.3 * angle D = 180 – 19;
2.3 * angle D = 161;
angle D = 161 / 2.3;
angle D = 70 degrees.
Then the angle B is equal to:
angle B = 0.3 * angle D = 0.3 * 70 = 21 (degree).
Answer: angle B = 21 degrees.
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