To find the value of \( x \) in the context of triangle \( ABC \), we know the following:
- The sum of the angles in a triangle is \( 180^\circ \).
- \( A = 26^\circ \)
- \( B = 4x + 45^\circ \)
- \( C = 47^\circ \)
We can use the formula for the sum of the angles in a triangle:
\[ A + B + C = 180 \]
Substituting the given values into the equation:
\[ 26 + (4x + 45) + 47 = 180 \]
Now, simplify the left side:
\[ 26 + 45 + 47 = 118 \]
So, we have:
\[ 118 + 4x = 180 \]
Next, isolate \( 4x \):
\[ 4x = 180 - 118 \] \[ 4x = 62 \]
Now, divide both sides by 4:
\[ x = \frac{62}{4} = 15.5 \]
Thus, the value of \( x \) is:
\[ \boxed{15.5} \]
1 answer