Question

unit 4 test
solve for x.
(9x + 1)°
88°

Explanation:

Step1: Identify triangle type

The triangle is isosceles as two sides are congruent. So the base - angles are equal. Let the base - angles be $y$. The sum of interior angles of a triangle is $180^{\circ}$. So, $(9x + 1)+y + y=180^{\circ}$. Since the base - angles are equal, and one base - angle is given as $y$, we know that the non - base angle is $88^{\circ}$ and the two base - angles are equal. So, $2y=180 - 88$.

Step2: Calculate base - angle value

$2y = 92^{\circ}$, then $y = 46^{\circ}$.

Step3: Solve for $x$

Set the expression for the base - angle equal to the calculated value. $9x+1 = 46$. Subtract 1 from both sides: $9x=46 - 1=45$. Divide both sides by 9: $x=\frac{45}{9}=5$.

Answer:

$x = 5$