Question

Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your reasoning.

Answer 1

The given angle and angle 3 are corresponding angles, that is, angles that are on the same corner at each intersection. Graphically,

Corresponding angles are congruent, so

`\angle3=95\text{\degree}`

On the other hand, angle 3 and angle 4 are supplementary angles, that is, add up to 180°. Graphically,

`A+B=180\text{\degree}`

So, you have

`\begin{gathered} \angle3+\angle4=180\text{\degree} \\ 95\text{\degree}+\angle4=180\text{\degree} \\ \text{ Subtract 95\degree from both sides of the equation} \\ 95\text{\degree}+\angle4-95\text{\degree}=180\text{\degree}-95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}`

Therefore, the measures of the numbered angles are

`\begin{gathered} \angle3=95\text{\degree} \\ \angle4=85\text{\degree} \end{gathered}`