The extended angle ABC was divided by the ray BD into two angles so that the degree measures of the angles ABD

| June 14, 2021 | education

The extended angle ABC was divided by the ray BD into two angles so that the degree measures of the angles ABD and CBD are related as 5:13. Find the degree measures of the angles ABD and CBD.

If angle ABC is a flat angle, then ∠ABC = 180 °. Angles ABD and CBD are adjacent angles. As you know, together, adjacent angles make up a deployed angle: ∠ABD + ∠CBD = 180 °. By the condition of the task, ∠ABD: ∠CBD = 5: 13. Applying the main property of proportion, we get: 13 * ∠ABD = 5 * ∠CBD, whence ∠ABD = (5/13) * ∠CBD. Substitute this into the expanded angle formula: (5/13) * ∠CBD + ∠CBD = 180 ° or (5/13 + 1) * ∠CBD = 180 °, whence ∠CBD = 180 °: (18/13) = 13 * 180 °: 18 = 130 °. Calculate ∠ABD = (5/13) * ∠CBD = (5/13) * 130 ° = 50 °. Thus, the degree measures of the angles ABD and CBD are 50 ° and 130 °, respectively.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.