Question

Question #0de9f

Answer 1

Starting with the known angles and parallel lines, use geometric properties to work through all the unknowns.

Explanation:

I won’t provide the entire solution, but rather the process that you can use to complete the exercise.

Given the parallel lines and the angle at E, the angle at K must be the same (`69^o`).
This leads to angle 12 being (180 – 69 – 90) = `21^o`.
From that, angle 8 must be 21 + 90 = `111^o`, and then the angle on the other side of it must be (180 - 111) = `69^o`.
EFG is an isosceles triangle, so angle 7 is also `69^o`, leading to angle 4 = (180 – 69 – 69) = `42^o`. Then angle 3 is (180 – 42 – 69) = `69^o` also.

Further, the angle at M is (180 – 90 – 21) = `69^o`. This is the same angle as that at G, so angle 8 is `111^o` also, and confirms our previous determination of angles 4 and 7.
Angle 9 is `116^o`, so angle 10 is `64^o`.

So far: Angle 3: `69^o` Angle 4: `42^o` Angle 5: ?? Angle 6: ?? Angle 7: `69^o` Angle 8: `111^o` Angle 9: `116^o` Angle 10: `64^o` Angle 11: ?? Angle 12: `21^o`

Continue on, using the angles you calculate with the properties of the parallel lines and triangles to calculate the remaining angles 5, 6 and 11