Question

Ребят помогите!Найдите смежные углы MKE и PKE,если угол FKE на 24° больше угла PKE, где луч KF-биссектриса угла MKE.

Answer 1

Угол FKE > угла PKE на 24 градуса
Углы MKE и PKE - смежные, следовательно их сумма равна 180 градусам ( по св-ву смежных углов)
Угол MKF= углу FKE (по определению биссектрисы угла)
Пусть угол PKE=х градусов, тогда
           угол FKE= углу MKF=(х+24) градусов
MKE+PKE=180 градусов
MKF+FKE+PKE=180 градусов
Зная это, составим уравнение
(х+24)+(х+24)+х=180
х+24+х+24+х=180
3х+48=180
3х=132
х=44
Угол PKE=44 градуса
Угол MKE= угол FKE+ угол MKF= (44+24)+(44+24)=136 градусов

Answer 2

Finding Adjacent Angles MKE and PKE

To find the measures of the adjacent angles MKE and PKE, we can use the given information that the angle FKE is 24° larger than the angle PKE, and that the ray KF is the bisector of the angle MKE.

Let's start by calculating the measure of angle PKE. Then, we can use the relationship between FKE and PKE to find the measure of angle FKE, and finally, determine the measure of angle MKE.

Calculating the Measure of Angle PKE

Given: - Angle FKE is 24° larger than angle PKE.

Let's assume the measure of angle PKE is x degrees. Then, the measure of angle FKE would be (x + 24) degrees.

Relationship between MKE and FKE

The ray KF is the bisector of angle MKE. This means that angle FKE and angle EKM are equal in measure.

Calculating the Measure of Angle MKE

Since the ray KF bisects angle MKE, we can conclude that angle FKE = angle EKM.

Now, we can express the measure of angle MKE in terms of x: - Angle MKE = 2 * angle EKM - Angle MKE = 2 * (x + 24)

So, the measure of angle MKE is 2 * (x + 24) degrees.

Conclusion

In summary: - The measure of angle PKE is x degrees. - The measure of angle FKE is (x + 24) degrees. - The measure of angle MKE is 2 * (x + 24) degrees.

This approach allows us to find the measures of the adjacent angles MKE and PKE based on the given information.