MATH SOLVE

4 months ago

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

Accepted Solution

A:

m ∠b = 133°, m ∠c = 47°, and m ∠d = 133°. Further explanationFollow 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 [tex]\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}[/tex]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. [tex]\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }[/tex][tex]\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }[/tex]Both sides subtracted by 47°.[tex]\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }[/tex]Thus [tex]\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}[/tex]Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, [tex]\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}[/tex]Conclusion:m ∠a = 47°m ∠b = 133°m ∠c = 47°m ∠d = 133°Notes:Supplementary angles are two angles when they add up to 180°. [tex]\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }[/tex]Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. [tex]\boxed{ \ example: \angle{a} = \angle{c} \ }[/tex]Learn moreAbout the measure of the central angle terms needed to define angles out the measures of the two angles in a right triangle : m∠a = 47°, m∠b, m∠c, and m∠d, 133°, vertical angles, supplementary, 180°, congruent