Question

"Прямые m и n пересекают четыре угла. Сумма градусных мер 1 и 3 углов равна 86º.Найдите градусные меры 2 и 4 углов"

Answer 1

86*2=172
360-172=128градусов

Answer 2

Solution for Finding the Measures of Angles 2 and 4

To find the measures of angles 2 and 4, we can use the information provided about the sum of the degrees of angles 1 and 3 being 86º.

Let's denote the measures of angles 1, 2, 3, and 4 as A, B, C, and D respectively.

Given: - m and n intersect four angles. - The sum of the degrees of angles 1 and 3 is 86º.

We can use the fact that when two lines intersect, the opposite angles are equal. This property is known as the "vertical angles theorem."

Using the vertical angles theorem, we can conclude that: - Angle 1 is equal to angle 3 (let's call this measure x).

Now, we can express the sum of the degrees of angles 1 and 3 in terms of x: - A + C = 86º - x + x = 86º - 2x = 86º - x = 43º

So, we have found that the measure of angle 1 (A) and angle 3 (C) is 43º.

Now, using the same reasoning, we can conclude that: - Angle 2 is equal to angle 4 (let's call this measure y).

Since angle 2 and angle 4 are equal, we can express the measure of angle 2 and angle 4 in terms of y: - B + D = 180º (as angles on a straight line add up to 180º) - B + B = 180º - 2B = 180º - B = 90º

Therefore, the measure of angle 2 (B) and angle 4 (D) is 90º.

So, the measure of angle 2 and angle 4 is 90º.