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2 years ago

A. Find the measure of m<1 B. Find the measure of m<1 ;m<2; m<3

Mathematics

1 answer:

natita [175]2 years ago

3 0

Answer:

A: m<1 = 79 degrees

B: m<1 = 61 degrees, m<2 = 151 degrees, m<3 = 12 degrees

Step-by-step explanation:

A: An exterior angle is equal to the sum of the two opposite interior angles. 27+52 in this case.

B: The sum of the measures of the interior angles in a triangle is 180 degrees.

Since we know the two angles in the right trinagle are 90 and 29 degrees, we add them and subract the sum from 180 which gives us 61 degrees.

Applying what we know from part A, 61 degrees+90 degrees = m<2.

And, since we know m<2 = 151 degrees, we add that and the 17 degrees to then subtract that sum from 180 to get the measure of angle 3 which is 12 degrees.

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Ooh, fun

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add (2r²+2r+2) to both sides
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solve using quadratic formula
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$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
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use them to solve for the value of a
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try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

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