Question

Хорды АВ и СD пересекаются в точке Е . Дуга АD = 54 градуса. Дуга ВС=70 градусов.Найти угол ВЕС.

Answer 1

Угол АСД=1\2АД=54:2=27°
Угол ВАС=1\2ВС=70:2=35°
В треугольнике АЕС угол Е=180-(27+35)=118°
Угол ВЕС=180°-118°=62°
Ответ: 62°

Answer 2

Problem Analysis

We are given that the chords AB and CD intersect at point E. The measure of arc AD is 54 degrees, and the measure of arc BC is 70 degrees. We need to find the measure of angle VES.

Solution

To find the measure of angle VES, we need to find the measure of arc VE and arc VS. Then, we can use the fact that the measure of an angle is equal to half the measure of its intercepted arc.

Let's start by finding the measure of arc VE. Since arc AD is 54 degrees, we can conclude that arc AE is also 54 degrees, as they are opposite arcs of the same chord. Similarly, since arc BC is 70 degrees, arc CE is also 70 degrees.

Now, let's find the measure of arc VS. Since arc AD is 54 degrees and arc BC is 70 degrees, the sum of arcs AD and BC is 54 + 70 = 124 degrees. Therefore, arc VS is equal to half of the sum of arcs AD and BC, which is 124/2 = 62 degrees.

Finally, we can find the measure of angle VES. Since angle VES is formed by arcs VE and VS, and we know the measures of these arcs, we can conclude that the measure of angle VES is equal to half the sum of the measures of arcs VE and VS. Therefore, angle VES = (arc VE + arc VS)/2.

Substituting the values we found earlier, angle VES = (54 + 62)/2 = 116/2 = 58 degrees.

Answer

The measure of angle VES is 58 degrees.