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lisov135 [29]
3 years ago
15

M<2 = 34. Find m<4 and explain how you know.

Mathematics
1 answer:
Basile [38]3 years ago
3 0

Answer:

m<4 = 34°

Step-by-step explanation:

m<2 = 34° (given)

m<3 + m<2 = 180° (linear pair)

m<3 + 34° = 180° (substitution)

Subtract 34° from each side

m<3 = 180° - 34°

m<3 = 146°

m<4 + m<3 = 180° (linear pair)

m<4 + 146° = 180° (substitution)

Subtract 146° from each side

m<4 = 180° - 146°

m<4 = 34°

This shows that vertical angles are congruent.

m<2 and m<4 are vertical angles formed when two straight line intersects. They are both of equal measure.

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\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)

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\bf \stackrel{IV~Quadrant}{b = -5}\qquad \qquad sin(B)=\cfrac{\stackrel{opposite}{-5}}{\underset{hypotenuse}{13}} \\\\[-0.35em] ~\dotfill\\\\ sin(A-B)=\cfrac{-4}{5}\cdot \cfrac{12}{13}-\left( \cfrac{3}{5}\cdot \cfrac{-5}{13} \right)\implies sin(A-B)=\cfrac{-48}{65} - \left( \cfrac{-15}{65} \right) \\\\\\ sin(A-B)=\cfrac{-48}{65} + \cfrac{15}{65}\implies sin(A-B)=\cfrac{-33}{65}

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