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

Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your-example-1
User Jonrsharpe
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1 Answer

21 votes
21 votes

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}

Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your-example-1
Use the figure to find the measures of the numbered angles. 95 23 24 = Explain your-example-2
User Gregory Klopper
by
3.2k points
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