If m∠a=47°, what is m∠b, m∠c, and m∠d? explain how you know the measures are correct.

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°.

Follow the attached picture. I sincerely hope that's precisely a correct illustration.

We will use a graph of two intersecting straight lines.

Note that m ∠a and m ∠c are vertical angles. Since vertical angles share the same measures, in other words always congruent, we see

We continue to determine m ∠b and m ∠d.

Note that m ∠b and m ∠d represent supplementary angles. Recall that supplementary angles add up to 180°.

Let us see the following steps.  

Both sides subtracted by 47°.

Thus

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly,

Conclusion:

Notes:

Keywords: m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent

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