To solve for the value of \( x \), we can set up the equation based on the information given:
- The sum of the measures of angle M and angle L is 116°.
- The measure of angle M is 50°.
- The measure of angle L is \( (7x - 4)° \).
We can set up the equation:
\[ 50 + (7x - 4) = 116 \]
Now, simplify the equation:
\[ 50 + 7x - 4 = 116 \] \[ 46 + 7x = 116 \]
Next, subtract 46 from both sides:
\[ 7x = 116 - 46 \] \[ 7x = 70 \]
Now, divide both sides by 7:
\[ x = \frac{70}{7} \] \[ x = 10 \]
Now let's check the answer by substituting \( x = 10 \) back into the measure of angle L:
\[ L = 7(10) - 4 = 70 - 4 = 66° \]
Now check the sum of angles M and L:
\[ M + L = 50 + 66 = 116° \]
The calculation checks out. Thus, the value of \( x \) is:
\[ \boxed{10} \]
None of the options A (1010), B (1212), C (1515), or D (20) matches the answer. It seems there might be a misunderstanding in the options presented.
2 answers