SOLUTION: Quadrilateral ABCD ~ quadrilateral HJKL. Two quadrilaterals are given side by side. The first quadrilateral appears smaller than the second. The first quadrilaterals has vertic

Question 1193596: Quadrilateral ABCD ~ quadrilateral HJKL.
Two quadrilaterals are given side by side. The first quadrilateral appears smaller than the second.
The first quadrilaterals has vertices A, B, C, and D.
The first side starts at vertex A, travels down and to the right, and ends at vertex B.
The second side appears horizontal, starts at the bottom left at vertex B, travels to the right, and ends at vertex C.
The third side starts at vertex C, travels up and to the left, and ends at vertex D.
The fourth side starts at vertex D, travels slightly down and to the left, and ends at vertex A.
∠A has 1 arc, ∠B has 2 arcs, ∠C has 3 arcs, and ∠D has 4 arcs.
The second quadrilateral has vertices H, J, K, and L.
The first side starts at vertex H, travels down and to the right, and ends at vertex J.
The second side appears horizontal, starts at the bottom left at vertex J, travels to the right, and ends at vertex K.
The third side starts at vertex K, travels up and to the left, and ends at vertex L.
The fourth side starts at vertex L, travels slightly down and to the left, and ends at vertex H.
∠H has 1 arc, ∠J has 2 arcs, ∠K has 3 arcs, and ∠L has 4 arcs.
If
m∠A = (2x + 3)°, m∠H = 69°, and m∠D = (3x − 9)°, find m∠L in degrees.
m∠L
=
°
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.


Hey, the idea of this problem is that the angles marked in the same way (having the same designations) are congruent,

i.e. have equal (degree) measure.


Therefore,  angle A = angle H, and you can write an equation

    2x + 3 = 69.


From this equation, find x;  then find the measures of angles A and D.


Angle L has the same measure as angle D.

Now you have all instructions, needed to you to complete the job on your own.

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