Question

PLEASE HURRY in below diagram, line bc is parallel to de. i.e bc de abc=47 cab=105 find cae

Answer 1

`\angle CAE=28`

Explanation:

`\angle CBA+\angle BAE=180\\\\\angle CBA+\angle BAC+\angle CAE=180\\\\47+105+?=180\\\\152+?=180\\\\?=28`

Answer 2

The measure of angle CAE is 28°

When there is a transversal across parallel line, the angles can be alternate , vertical or corresponding and in each case they are equal.

Line DE is parallel to line BC

therefore angle BAD = 47° ( alternate angles)

angle BAD , BAC and CAE are on a straight line , this means that the sum of these angles will be 180°

let CAE be x

Therefore;

47 + 105 + x = 180

x = 180 - ( 105 +47)

x = 180 - 152

x = 28°

Therefore the measure of angle CAE is s 28°