Question

2. Січна перетинає дві прямі, при цьому утворились односторонні кути, різниця яких дорівнює 36°, а відношення 3:2. Довести, що прямі паралельні​

Answer 1

кут 1, є меншим =х, кут 2= х+36, кут2 / кут1= 3/2 і х+36/х=3/2, 3х=2х+72 і х=72 і 72+36=108, 72+108=180 - якщо при перетині двох прямих третьої сума односторонніх кутів дорівнює 180 градусам, значить то прямі паралельні.

Answer 2

Given Information:

We are given that two lines intersect and form one-sided angles with a difference of 36°, and the ratio of these angles is 3:2. We need to prove that the lines are parallel.

Solution:

To prove that the lines are parallel, we need to show that the alternate interior angles are congruent.

Let's assume that the two lines are represented by line l1 and line l2, and the angles formed by the intersection are angle A and angle B.

According to the given information, the difference between angle A and angle B is 36°, and the ratio of angle A to angle B is 3:2.

Let's represent angle A as 3x and angle B as 2x.

Therefore, we have the following equation: 3x - 2x = 36°

Simplifying the equation, we get: x = 36°

Now, we can find the measures of angle A and angle B: Angle A = 3x = 3 * 36° = 108° Angle B = 2x = 2 * 36° = 72°

Since angle A and angle B are alternate interior angles, and their measures are congruent to 108° and 72° respectively, we can conclude that the lines l1 and l2 are parallel.

Therefore, we have proved that the lines are parallel.

Note: The given information does not provide enough context or equations to solve the problem completely. The solution provided assumes that the angles formed by the intersection are alternate interior angles. If there is additional information or context, please provide it for a more accurate solution.