Question

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

ZB = (2x – 15)°, then find the measure of ZA.

Answer 1

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

According to the question

`\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 \: = \: (126)/(3) \\`

`\bf \large \longrightarrow \: \:x \: = \: \cancel(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°

Answer 2

A = 21

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