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4 years ago

If angle 1 = 10x + 4 and angle 2 = 5x – 4, find angle 2 a.)56 b.)78 c.)12 d.)65

Mathematics

1 answer:

Semenov [28]4 years ago

8 0

Angle 1 and 2 are supplementary angles, meaning they must add up to 180°. You can tell this because they share a side and together, their other side forms a straight line (and straight lines are 180°).

Knowing this, you can make an equation to solve for x:
Angle 1 + Angle 2 = 180°
10x + 4 + 5x – 4 = 180°
15x = 180°
x = 12°

Knowing x = 12°, you can plug the value of x into the equation for angle 2 to find its measurement:
Angle 2 = 5x – 4
Angle 2 = 5(12°) - 4
Angle 2 = 56°

--------

Answer: A) 56°

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$\implies {\pink {\boxed {\boxed {\purple {\sf { \: x = \frac{2}{7}}}}}}}$

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Let $x$ be the unknown number.

As per the question, we have

$\: ( \frac{3}{7} \times \frac{2}{5} ) - x = \frac{ - 4}{35}$

➺ $\: \frac{6}{35} - x = \frac{ - 4}{35}$

➺ $\: - x = \frac{ - 4}{35} - \frac{6}{35}$

➺ $\: - x = \frac{ - 4 - 6}{35}$

➺ $\: - x = \frac{ - 10}{35}$

➺ $\: x = \frac{2}{7}$

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$\large\mathfrak{{\pmb{\underline{\orange{To\:verify}}{\orange{:}}}}}$

$\: ( \frac{3}{7} \times \frac{2}{5} ) - x = \frac{ - 4}{35}$

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Make use of the fact that:

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