Question

Complementary and

What is the measure of Zx?
Angles are not necessarily drawn to scale.
P.
R
48
20
Q
S
2

Answer 1

The measurement of x is 42⁰.

Step-by-step explanation:

SOLUTION :

Here, we can see that the given figure is complementary angle.

As we know that two angles are said to be complementary angles if they add up to 90 degrees.

Now, according to the question :

`\longmapsto{\sf{Sum \: of \: two \: angles = {90}^( \circ)}}`

`\longmapsto{\sf{Angle_1 + Angle_2 = {90}^( \circ)}}`

`\longmapsto{\sf{{48}^( \circ) + {x}^(\circ) = {90}^( \circ)}}`

`\longmapsto{\sf{{x}^(\circ) = {90}^( \circ) - {48}^(\circ) }}`

`\longmapsto{\sf{{x}^(\circ) = {42}^(\circ) }}`

`\star{\underline{\boxed{\sf{\pink{{x}^(\circ) = {42}^(\circ)}}}}}`

Hence, the measurement of x is 42⁰.

`\rule{300}{2.5}`

Answer 2

`\boxed{\boxed{\sf x=42\°}}`

Explanation:

Given the diagram, we can see that ∠PQR and ∠RQS are complementary angles.

*Two angles with measures that add up to 90° are known as Complementary angles.*

Therefore, m∠PQR+m∠RQS=90°

`\sf \angle PQR+\angle RQS=90\°`

`\sf 48+x=90\°`

Subtract 48 from both sides:

`\sf 48+x-48=90-48`

`\sf x=42\°`

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