ZJ and ZK are complementary angles.The measure of ZJ is 18 less than themeasure of ZK. Find the measure of eachangle.Answer please

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26-10-2022
Mathematics

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ZJ and ZK are complementary angles.The measure of ZJ is 18 less than themeasure of ZK. Find the measure of eachangle.Answer please

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IzekielN321685 IzekielN321685 · Answer 1 · 2022-10-26T16:05:09+02:00

ANSWER:

ZK = 54°

ZJ = 36°

STEP-BY-STEP EXPLANATION:

We can raise the following equations because we know that the angles are complementary:

[tex]\begin{gathered} ZJ+ZK=90\text{\degree} \\ ZJ=ZK-18\text{\degree} \end{gathered}[/tex]

Replacing:

[tex]\begin{gathered} ZK-18+ZK=90 \\ 2ZK=90+18 \\ ZK=\frac{108}{2} \\ ZK=54\text{\degree} \\ \text{ therefore, ZJ is:} \\ ZJ=54-18 \\ ZJ=36\text{\degree} \end{gathered}[/tex]