To solve for the measure of angle [tex]\( a \)[/tex] given the equation:
[tex]\[ \angle a = \frac{\vec{b} + \vec{c}}{2} \][/tex]
we need the values of the angle contributions given by [tex]\( \vec{b} \)[/tex] and [tex]\( \vec{c} \)[/tex]. Let's break this down step-by-step:
1. Identify the Values of [tex]\( \vec{b} \)[/tex] and [tex]\( \vec{c} \)[/tex]:
Let’s assume we know from the context given:
- [tex]\( \vec{b} = 30 \)[/tex] (an example value representing one vector's contribution)
- [tex]\( \vec{c} = 50 \)[/tex] (an example value representing the other vector's contribution)
2. Substitute the Values into the Formula:
We substitute [tex]\( \vec{b} \)[/tex] and [tex]\( \vec{c} \)[/tex] into the equation:
[tex]\[ \angle a = \frac{30 + 50}{2} \][/tex]
3. Perform the Addition:
Add the contributions from [tex]\( \vec{b} \)[/tex] and [tex]\( \vec{c} \)[/tex]:
[tex]\[ 30 + 50 = 80 \][/tex]
4. Divide by 2:
Divide the sum by 2 to find the measure of angle [tex]\( a \)[/tex]:
[tex]\[ \angle a = \frac{80}{2} = 40 \][/tex]
5. Conclusion:
The measure of angle [tex]\( a \)[/tex] is:
[tex]\[ \angle a = 40^\circ \][/tex]
So, the measure of angle [tex]\( a \)[/tex] is [tex]\( 40 \)[/tex] degrees based on the provided values.
