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3 years ago

Can someone help please show steps

Mathematics

1 answer:

NikAS [45]3 years ago

4 0

Hello!

$\large\boxed{-16}$

Use PEMDAS (order of operations) to solve:

-4 · [3 + (-5)²] ÷ 7

Square -5:

-4 · [3 + 25] ÷ 7

Add the numbers inside of the parenthesis:

-4 · [28] ÷ 7

Multiply -4 and 28:

-112 ÷ 7

Divide:

= -16.

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Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65°. Find: m∠LMW

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Answer:

The measure of angle LMW is $m\angle LMW=67\°$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

$m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK]$

substitute the given values

$65\°=\frac{1}{2}[arc\ MW+68\°]$

$130\°=[arc\ MW+68\°]$

$arc\ MW=130\°-68\°=62\°$

step 2

Find the measure of arc LK

we know that

$arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°$ -----> by complete circle

substitute the given values

$164\°+62\°+68\°+arc\ LK=360\°$

$294\°+arc\ LK=360\°$

$arc\ LK=360\°-294\°=66\°$

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

$m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK]$

substitute the given values

$m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°$

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