Question

identify x then find the missing angle measurements (13x - 21)° (5x + 75)°

Explanation:

Step1: Set up equation

Since the two given angles are corresponding angles (assuming lines $l$ and $m$ are parallel) and corresponding angles are equal, we set up the equation $13x - 21=5x + 75$.

Step2: Solve for $x$

Subtract $5x$ from both sides: $13x-5x - 21=5x-5x + 75$, which simplifies to $8x-21 = 75$. Then add 21 to both sides: $8x-21 + 21=75 + 21$, getting $8x=96$. Divide both sides by 8: $x=\frac{96}{8}=12$.

Step3: Find angle measures

For the first angle, substitute $x = 12$ into $13x - 21$: $13\times12-21=156 - 21=135^{\circ}$. For the second angle, substitute $x = 12$ into $5x + 75$: $5\times12+75=60 + 75=135^{\circ}$.

Answer:

$x = 12$, the angles are $135^{\circ}$ and $135^{\circ}$