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loris [4]
2 years ago
10

ZA and ZB are complementary angles. If m A = (x – 21)° and m

Mathematics
2 answers:
pogonyaev2 years ago
7 0

Answer:

A = 21

Step-by-step explanation:

Complementary angles add to 90

x-21 + 2x-15 = 90

Combine like terms

3x -36 = 90

3x-36+36 = 90+36

3x = 126

Divide by 3

3x/3 =126/3

x = 42

We want to find ZA = x-21

A = 42-21

A = 21

Lelu [443]2 years ago
4 0

If the sum of the measures of two angles is 90° they are known as complementary angles.

<h3 /><h3>According to the question</h3>

\bf \large \longrightarrow \:  \:( x \:  -  \: 21) \:  +  \: (2x \:  -  \: 15) \:  =  \: 90 \degree

Now , Opening brackets and simplifying

\bf \large \longrightarrow \:  \: x \:  -  \: 21 \:  +  \: 2x \:  -  \: 15\:  =  \: 90 \degree

\bf \large \longrightarrow \:  \:3x \:  -  \: 36 \:  =  \: 90 \degree

\bf \large \longrightarrow \:  \:3x \:  =  \: 90 \: +  \: 36

\bf \large \longrightarrow \:  \:3x \:  =  \: 126

\bf \large \longrightarrow \:  \:x \:  =  \:  \frac{126}{3}  \\

\bf \large \longrightarrow \:  \:x \:  =  \:   \cancel\frac{126}{3}   \: \:  \large \: ^{42}  \\

\bf \large \longrightarrow \:  \: x \:  =  \: 42

Now , we have to find ZA .

  • ZA = x - 21

\bf \large \implies \:  \:A \:  =  \: 42 \:  -  \: 21

\bf \large \implies \:  \:A \:  =    \: 21

The measure of angle ZA is 21°

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