# Question #0de9f

Feb 3, 2017

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