Question

Відрізки AB i CD перетинаються у точці O, яка є серединою кожного з них. Чому дорівнює градусна міра кута ACB, якщо кут СBD = 68 градусів?

Answer 1

Відповідь:

Пояснення:

 Сполучивши послідовно кінці даних відрізків , одержимо

 паралелограм ABCD , у якого   ∠СBD = 68° . Тоді

 ∠ACB = 180° - ∠СBD = 180° - 68° = 112° ;    ∠ACB = 112° .

Answer 2

Given Information:

We are given that the line segments AB and CD intersect at point O, which is the midpoint of both segments. We are also given that the measure of angle CBD is 68 degrees.

Solution:

To find the measure of angle ACB, we can use the fact that O is the midpoint of both line segments AB and CD. This means that AO = BO and CO = DO.

Since O is the midpoint of AB, we can draw a line segment from O to the midpoint of AB, which we'll call E. Similarly, we can draw a line segment from O to the midpoint of CD, which we'll call F.

Now, we have two congruent triangles: triangle AOE and triangle COF. This is because AO = CO (both are half the length of AB), OE = OF (both are half the length of CD), and angle AEO = angle CFO = 90 degrees (both are right angles).

Since the triangles are congruent, their corresponding angles are also congruent. Therefore, angle AEO is congruent to angle CFO.

Now, let's consider triangle ACO. We have angle ACO, which is the same as angle AEO, and angle CBD, which is the same as angle CFO. Since angle AEO and angle CFO are congruent, we can conclude that angle ACO and angle CBD are also congruent.

Therefore, the measure of angle ACB is equal to the measure of angle CBD, which is 68 degrees.

Answer: The measure of angle ACB is 68 degrees.