Question

из вершины развёрнутого угла абц проведите луч луч бд, так чтобы градусная мера угла абд была была в 5раз меньше градусной меры угла цбд.чему равны градусные меры углов абц и цбд?

Answer 1

Ответ:

Пошаговое объяснение:

Развёрнутый угол = 180°

угол АБД = х°

угол ЦБД = 5х°

х + 5х = 180

6х = 180

х = 180 : 6

х = 30

АБД (х) = 30°

ЦБД (5х) = 5 * 30 = 150°

30° + 150° = 180°

Answer 2

To find the degrees of angles ABC and CBD, we need to use the given information that the degree measure of angle ABD is 5 times smaller than the degree measure of angle CBD. Let's solve this step by step.

Step 1: Identify the given information

- The degree measure of angle ABD is 5 times smaller than the degree measure of angle CBD.

Step 2: Assign variables

- Let x be the degree measure of angle CBD.

Step 3: Express the degree measure of angle ABD in terms of x

- Since the degree measure of angle ABD is 5 times smaller than the degree measure of angle CBD, we can express it as 5x.

Step 4: Find the degree measure of angle ABC

- The sum of the degree measures of angles in a triangle is always 180 degrees. Therefore, we can write the equation: angle ABC + angle BAC + angle ACB = 180 degrees. - Since angle BAC and angle ACB are right angles (90 degrees each) in this case, we can simplify the equation to: angle ABC + 90 degrees + 90 degrees = 180 degrees. - Simplifying further, we get: angle ABC = 180 degrees - 90 degrees - 90 degrees = 0 degrees.

Step 5: Find the degree measure of angle CBD

- We know that angle ABD is 5 times smaller than angle CBD. Therefore, we can write the equation: 5x + x + 90 degrees = 180 degrees. - Simplifying the equation, we get: 6x + 90 degrees = 180 degrees. - Subtracting 90 degrees from both sides, we get: 6x = 90 degrees. - Dividing both sides by 6, we get: x = 15 degrees.

Step 6: Find the degree measure of angle ABD

- We know that angle ABD is 5 times smaller than angle CBD. Therefore, angle ABD = 5x = 5 * 15 degrees = 75 degrees.

Step 7: Final answer

- The degree measure of angle ABC is 0 degrees. - The degree measure of angle ABD is 75 degrees. - The degree measure of angle CBD is 15 degrees.

Therefore, the degree measures of angles ABC and CBD are 0 degrees and 15 degrees, respectively.