Question

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

Answer 1

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

Further explanation

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 $\boxed{ \ m \ \angle{c} = m \ \angle{a} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{c} = 47^0 \ }}$

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.  

$\boxed{ \ m \ \angle{a} + m \ \angle{b} = 180^0. \ }$

$\boxed{ \ m \ 47^0 + m \ \angle{b} = 180^0. \ }$

Both sides subtracted by 47°.

$\boxed{ \ m \ \angle{b} = 180^0 - 47^0. \ }$

Thus $\boxed{\boxed{ \ m \ \angle{b} = 133^0. \ }}$

Finally, note that m ∠b and m ∠d are vertical angles. Accordingly, $\boxed{ \ m \ \angle{d} = m \ \angle{b} \ } \rightarrow \boxed{\boxed{ \ m \ \angle{d} = 133^0 \ }}$

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°. $\boxed{ \ example: \angle{a} + \angle{b} = 180^0 \ }$
• Vertical angles are the angles opposite each other when two lines cross. Note that vertical angles are always congruent, or of equal measure. $\boxed{ \ example: \angle{a} = \angle{c} \ }$

Learn more

1. About the measure of the central angle brainly.com/question/2115496
2. Undefined terms needed to define angles  brainly.com/question/3717797
3. Find out the measures of the two angles in a right triangle brainly.com/question/4302397

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

Answer 2

m ∠d = 133°

m ∠c = 47°

m ∠b = 133°

Further explanation

Assuming there are two planes that intersect, the total sum of all angles will be 360°.

This means that m ∠a+ m ∠b+ m ∠c+ m ∠d=360°.

If the planes intersect then m ∠a is congruent to m ∠c and supplementary to m ∠b, meaning that m ∠a = m ∠c and m ∠a + m ∠b = 180°

Therefore, to determine m ∠b,  

180°– 47° = m ∠b

m ∠b = 133°

since m ∠a = m ∠c, then m ∠b= m ∠d

therefore,  

   m ∠a = 47°

   m ∠b = 133°

   m ∠c = 47°

   m ∠d = 133°

About Question:

Subject : Mathematics

level:Middle  School

Related Links:

brainly.com/question/12869448