Given: m∠p =47BD∥AC What is the m∠m? Put only the number. Do not label your answer.

Mathematics

1 answer:

Anettt [7]3 years ago

3 0

Answer: $43\°$

Step-by-step explanation:

Observe the given figure.

You can identify that the measure of the angle "B" is:

$m\angle B=90\°$

Knowing this, you can conclude that the angle "p" and the angle "m" are Complementary angles, which means that the sum of their measures is 90 degrees. Then, you can write the following equation:

$m\angle p+m\angle m=90\°$ [Equation 1]

You know that:

$m\angle p=47\°$

Then you can substitute it into the [Equation 1] and then solve for $m\angle m$ . Therefore, you get:

$47\°+m\angle m=90\°\\\\m\angle m=90\°-47\°\\\\m\angle m=43\°$

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Step-by-step explanation:

$\bold{METHOD\ 1}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=\dfrac{8}{6}e\to d=\dfrac{4}{3}e\\\\\text{Substitute it and}\ f=2e\ \text{to the ratio}\ d:e:f:\\\\\dfrac{4}{3}e:e:2e\qquad\text{cancel}\ e\\\\\dfrac{4}{3}:1:2\qquad\text{multiply by 3}\\\\\huge\boxed{4:3:6}$

$\bold{METHOD\ 2}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=\dfrac{8}{6}e\qquad\text{divide both sides by}\ e\neq0\\\\\dfrac{d}{e}=\dfrac{4}{3}\to d:e=4:3\\\\2e=f\qquad\text{divide both sides by 2}\\\\e=\dfrac{f}{2}\to e=\dfrac{1}{2}f\qquad\text{divide both sides by}\ f\neq0\\\\\dfrac{e}{f}=\dfrac{1}{2}\to e:f=1:2\\\\\text{We have}\ d:e=4:3\ \text{and}\ e:f=1:2.$

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