M11 | Maths Made Easy

M11

Question: CF and GJ are parallel lines. Find the angle marked x in the diagram. State which angle fact you use at each step.

 

Answer: Firstly, because angles BEF and EHJ are corresponding angles, we get

\text{angle EHJ } = 39\degree.

Next, because angles EDH and DHG are alternate angles, we get

\text{angle DHG } = 76\degree.

Then, because angles DHG, DHE, and EHJ are angles on a straight line and angles on a straight line add to 180\degree, we get

\text{angle DHE } = 180 - 76 - 39 = 65\degree

Finally, because angle DHE and angle x are vertically opposite angles, we get

x = 65\degree.