Question

construct an angle of 145​

Answer 1

Step-by-step explanation:

Here is a way with a markable ruler and compass.

1.construct a 30 degree angle (bisect an equilateral triangle) and call the vertex O

2.draw a circle with centre O and call where it meets the sides of the angle A and B

3.mark the ruler with the radius of the circle

4.extend the line segment AO beyond O, calling where it meets the circle again C, and then extend the line further beyond C

5.place the ruler so that it touches B, and so that it cuts the circle again and the extended line the distance apart marked on the ruler, then draw the line and calling these points D and E respectively

6.use what you know about angles and the isosceles triangles BOD and ODE to find the angle OED (10 degrees)

7.add a right angle (90 degrees) and half a right angle (45 degrees) at E to get a total angle of 145 degrees (10+90+45).