Question

Четырехугольник ABCD вписан в окр. Угол ABC равен 80` угол CAD 54` Найти угол ABD ответ в градусах

Answer 1

Угол АВС =1/2дугиАСД, дуга АСД=2*уголАВС=2*80=160
уголСАД=1/2дугиСД, дуга СД=2*уголСАД=54*2=108
уголАВД=1/2дугиАД, дугаАД=дугаАДС-дугаСД=160-108=52
уголАВД=52/2=26

Answer 2

Given Information:

We are given a quadrilateral ABCD inscribed in a circle. The measure of angle ABC is 80 degrees, and the measure of angle CAD is 54 degrees. We need to find the measure of angle ABD in degrees.

Solution:

To find the measure of angle ABD, we can use the property that the measure of an angle inscribed in a circle is half the measure of its intercepted arc.

Let's denote the measure of arc BC as x. Since ABCD is a quadrilateral inscribed in a circle, the opposite angles of the quadrilateral are supplementary. Therefore, the measure of arc AD is also x.

According to the given information, the measure of angle ABC is 80 degrees. This means that the measure of arc BC is also 80 degrees. Similarly, the measure of angle CAD is 54 degrees, which means that the measure of arc AD is also 54 degrees.

Now, we can set up an equation using the property mentioned earlier:

Measure of angle ABD = (Measure of arc BC - Measure of arc AD) / 2

Substituting the values we have:

Measure of angle ABD = (80 - 54) / 2 = 26 / 2 = 13 degrees

Therefore, the measure of angle ABD is 13 degrees.

Answer:

The measure of angle ABD is 13 degrees.