Sure, let's break down each part of the problem step by step.
### 7. a) Finding the Complement of 30 Degrees
The complement of an angle [tex]\( \theta \)[/tex] is given by [tex]\( 90^\circ - \theta \)[/tex].
1. Here, [tex]\( \theta = 30^\circ \)[/tex].
2. To find the complement, we calculate:
[tex]\[
90^\circ - 30^\circ = 60^\circ
\][/tex]
So, the complement of [tex]\( 30^\circ \)[/tex] is [tex]\( 60^\circ \)[/tex].
### 7. b) If [tex]\( 7x^\circ \)[/tex] and [tex]\( 2x^\circ \)[/tex] form a linear pair, find the value of [tex]\( x \)[/tex]
A linear pair of angles sums up to [tex]\( 180^\circ \)[/tex].
1. Given angles are [tex]\( 7x^\circ \)[/tex] and [tex]\( 2x^\circ \)[/tex].
2. Therefore, the equation will be:
[tex]\[
7x + 2x = 180^\circ
\][/tex]
3. Simplify the equation:
[tex]\[
9x = 180^\circ
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{180}{9} = 20
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 20 \)[/tex].
### Summary
- The complement of [tex]\( 30^\circ \)[/tex] is [tex]\( 60^\circ \)[/tex].
- If [tex]\( 7x^\circ \)[/tex] and [tex]\( 2x^\circ \)[/tex] form a linear pair, the value of [tex]\( x \)[/tex] is [tex]\( 20 \)[/tex].
