Question

11
$\angle j$ and $\angle p$ are complementary angles.
$m\angle j = 6x + 1$ $m\angle p = 5x + 1$
write the equation:
$x = $
$m\angle p = $ degrees

Explanation:

Step1: Define complementary angles sum

Complementary angles sum to $90^\circ$, so set up the equation:
$$(6x + 1) + (5x + 1) = 90$$

Step2: Simplify left side of equation

Combine like terms:
$$11x + 2 = 90$$

Step3: Isolate the variable term

Subtract 2 from both sides:
$$11x = 88$$

Step4: Solve for $x$

Divide both sides by 11:
$$x = \frac{88}{11} = 8$$

Step5: Calculate $m\angle P$

Substitute $x=8$ into $m\angle P = 5x + 1$:
$$m\angle P = 5(8) + 1 = 41$$

Answer:

Write the equation: $\boldsymbol{(6x + 1) + (5x + 1) = 90}$
$x = \boldsymbol{8}$
$m\angle P = \boldsymbol{41}$ degrees