The opposite angles of an inscribe quadrilateral are supplementary.
angle P + angle R = 180
6x + 7 + 12x + 11 = 180
18x + 18 = 180
18x = 162
x = 9
Now we will substitute in the value of x to find angle P and R.
angle P = 6(9)+7 = 61
angle R = 12(9)+11 = 119
Now we will find the value of y.
angle Q + angle S = 180
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 152
y = 8
Now substitute in the value of y to find angle Q and S.
angle Q = 10(8)+7 = 87
angle S = 3(3*8+7) = 93
Hope this helps :)
Lemme think real quick...
<h3>
<u>Answer:</u></h3>

<h3>
<u>Step-by-step explanation:</u></h3>
A figure is given to us in which we can see two triangles one is ∆ MPL and other is ∆MPN .
<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>



Hence by SAS congruence condition ,
Hence by cpct ( Corresponding parts of congruent triangles ) we can say that , LM = NM = 11 units .
<h3>
<u>Hence </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>LM</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>units</u><u> </u><u>.</u></h3>