Question

ПОМОГИТЕ ПОЖАЙЛУСТА.Найдите угол CDB, если вписанные углы ADB и ADC опираются на дуги окружности, градусные величины которых равны соответственнот 166 и 88 градусов. Ответ дайте в градусах.РАСПИШИТЕ ПОЖАЛУЙСТА ПОДРОБНО.

Answer 1

уголCDB=(166-88)/2=39

Answer 2

To find the angle CDB, we need to consider the angles ADB and ADC, which are inscribed angles that rely on the arcs of a circle. The given degree measures for these arcs are 166 and 88 degrees, respectively.

Inscribed Angles and Arcs

Inscribed angles are formed by two chords or secants that intersect on the circumference of a circle. The measure of an inscribed angle is equal to half the measure of its intercepted arc. This property can be used to find the measure of angle CDB.

Finding the Measure of Angle CDB

To find the measure of angle CDB, we need to determine the measure of the intercepted arc by angle ADB. Since the measure of the intercepted arc is given as 166 degrees, we can conclude that the measure of angle ADB is twice that, or 332 degrees. Similarly, the measure of angle ADC is twice the measure of the intercepted arc, which is 176 degrees.

Now, we can find the measure of angle CDB by subtracting the sum of angles ADB and ADC from 360 degrees. Let's calculate it:

Measure of angle CDB = 360 degrees - (Measure of angle ADB + Measure of angle ADC)
                    = 360 degrees - (332 degrees + 176 degrees)
                    = 360 degrees - 508 degrees
                    = -148 degrees

Therefore, the measure of angle CDB is -148 degrees.

Please note that angles are typically measured in positive degrees, so a negative angle may not be a valid result. It is possible that there might be an error in the given information or in the calculations.