Question

P Q R S T U is a regular hexagon determine is angle of triangle PQT

Answer 1

I have attached a photo. Hope you can open it. The triangle is a right triangle with angle qpt being 90
The angle pqt 60 and angle ptq 30
To solve this problem draw the shape. Each angle of hexagon is 120. In triangle TUP we know U is 120. Therefore the small angles of T and P each is 30 since 120+30+30 =180
If small P is 30 and the whole P is 120 therefore the angle TPq should be right angle which is 120-30 = 90
Now look at the trapezoid
Rsqt. This is 360 degrees. If s and r are 120 each then the angle stq Should be 60. The same as angle rqt. If rqt is 60 and the whole q is 120 then the angle tqp should be 120-60=60
Then the angle qtp should be 30 since the triangle is right angle and one of the angles is 60 then the other one is supposed to be 30