Question

fill in the blank 1 point
7.
$m\angle m = \underline{\quad\quad}$
$m\angle n = \underline{\quad\quad}$
$m\angle o = \underline{\quad\quad}$
$m\angle p = \underline{\quad\quad}$
$m\angle m = $ type your answer...
$m\angle n = $ type your answer...
$m\angle o = $ type your answer...
$m\angle p = $ type your answer...

Explanation:

Step1: Identify trapezoid angle property

In a trapezoid, consecutive angles between the bases are supplementary, so $\angle M + \angle P = 180^\circ$ and $\angle N + \angle O = 180^\circ$. Also, $\angle M$ and $\angle N$ are same-side interior angles for transversal $MN$, so $\angle M + \angle N = 180^\circ$.

Step2: Set up equation for $x$

$(6x - 16) + (4x + 20) = 180$
Simplify: $10x + 4 = 180$

Step3: Solve for $x$

$10x = 180 - 4 = 176$
$x = \frac{176}{10} = 17.6$

Step4: Calculate $m\angle M$

Substitute $x=17.6$ into $6x-16$:
$m\angle M = 6(17.6) - 16 = 105.6 - 16 = 89.6^\circ$

Step5: Calculate $m\angle N$

Substitute $x=17.6$ into $4x+20$:
$m\angle N = 4(17.6) + 20 = 70.4 + 20 = 90.4^\circ$

Step6: Calculate $m\angle P$

Since $\angle M + \angle P = 180^\circ$:
$m\angle P = 180 - 89.6 = 90.4^\circ$

Step7: Calculate $m\angle O$

Since $\angle N + \angle O = 180^\circ$:
$m\angle O = 180 - 90.4 = 89.6^\circ$

Answer:

$m\angle M = 89.6^\circ$
$m\angle N = 90.4^\circ$
$m\angle O = 89.6^\circ$
$m\angle P = 90.4^\circ$