Question

Use the diagram to calculate the measure of angle 5

Answer 1

m∠5=22 °

Explanation:

In the diagram:

• Angles 4 and 90 degrees, are ,vertical angles,.

,

• Angles 2 and 68 degrees, are ,vertical angles,.

Since the measure of vertical angles is equal:

`\begin{gathered} m\angle4=90\degree \\ m\angle2=68\degree \end{gathered}`

In the triangle:

`m\angle2+m\angle4+m\angle5=180\degree\text{ (sum of angles }in\text{ a triangle)}`

Substitute the measures of angle 2 and 4 obtained earlier:

`\begin{gathered} 90\degree+68\degree+m\angle5=180\degree \\ 158\degree+m\angle5=180\degree \\ Subtract\text{ }158\degree\text{ from both sides of the equation.} \\ m\angle5=180\degree-158\degree \\ m\angle5=22\degree \end{gathered}`

The measure of angle 5 is 22 degrees.