hi and welcome to the session let us discuss the following question question says if tan 2a is equal to cut a minus 18 degrees where two ways an acute angle find the value of e first of all let us understand that what 90 minus theta is equal to tan theta where theta is any acute angle in a right triangle this is the key idea to solve the given question let us now start with the solution we are given time to wait is equal to what a minus 18 degrees now we know toy is an acute angle and we also know that tan theta is equal to call 90 minus theta here value of theta is equal to 2 it so we can write tan 2a is equal to what 90 degrees minus 2i so we can write this implies part 90 degrees minus 2a is equal to hot a minus 18 degrees now for 90 degrees minus 2a is equal to cut a minus 18 degrees only when value of these two angles is equal so this implies 90 degrees minus 2a is equal to a minus 18 degrees now adding 18 degrees on both the sides we get 108 degrees minus 2a is equal to in how adding two women both the sides we get 108 degrees is equal to 3 now dividing both the sides by 3 we get 36 degrees is equal to a or we can simply write it as a is equal to 36 degrees so our required answer is angle a is equal to 36 degrees this completes the session hope you understood position take care I'll have a nice day