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3 years ago

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One angle of a triangle measures 120°. The other two angles are in a ratio of 5:7. What are the measures of those two angles

1 answer:

natta225 [31]3 years ago

3 0

5x= one angle measure
7x= second angle measure
120°= third angle

Triangles equal 180°. Add the angles above to total 180°. Find x to find two two unknown angles.

5x + 7x + 120°= 180°
combine like values

12x + 120= 180
subtract 120 from both sides

12x= 60
divide both sides by 12

x= 5

ONE ANGLE MEASURE
5x= 5(5)= 25°

SECOND ANGLE MEASURE
7x= 7(5)= 35°

CHECK:
25° + 35° + 120°= 180°
180°= 180°

ANSWER: The measures of the two angles are 25° and 35°.

Hope this helps! :)

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Step-by-step explanation:

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Step-by-step explanation:

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Anuta_ua [19.1K]

Answer:

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Step-by-step explanation:

We are asked to divide our given fraction: $\frac{45^{45}*15^{15}}{75^{30}}$ .

We will simplify our division problem using rules of exponents.

Using product rule of exponents $(a*b)^n=a^n*b^n$ we can write:

$45^{45}=(3*15)^{45}=3^{45}*15^{45}$

$75^{30}=(5*15)^{30}=5^{30}*15^{30}$

Substituting these values in our division problem we will get,

$\frac{3^{45}*15^{45}*15^{15}}{5^{30}*15^{30}}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$\frac{3^{45}*15^{45+15}}{5^{30}*15^{30}}$

$\frac{3^{45}*15^{60}}{5^{30}*15^{30}}$

Using quotient rule of exponent $\frac{a^m}{a^n}=a^{m-n}$ we will get,

$\frac{3^{45}*15^{60-30}}{5^{30}}$

$\frac{3^{45}*15^{30}}{5^{30}}$

Using product rule of exponents $(a*b)^n=a^n*b^n$ we will get,

$\frac{3^{45}*(3*5)^{30}}{5^{30}}$

$\frac{3^{45}*3^{30}*5^{30}}{5^{30}}$

Upon canceling out $5^{30}$ we will get,

$3^{45}*3^{30}$

Using power rule of exponents $a^m*a^n=a^{m+n}$ we will get,

$3^{45+30}$

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Therefore, our resulting quotient will be $3^{75}$ .

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