Agreeting card company is creating musically themed greeting cards. the image below shows a music symbol that will be used on one of the cards, with several labeled angles. lines 1 and 2 in the image are parallel. enter the degree measure of ∠k.

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Agreeting card company is creating musically themed greeting cards. the image below shows a music symbol that will be used on one of the cards, with several labeled angles. lines 1 and 2 in the image are parallel. enter the degree measure of ∠k.

Measure of angle K is 77 degrees.

Step-by-step explanation:

We are told lines 1 and 2 are parallel in the given image.

Now we will use alternate exterior angles theorem which states that angles that are on the exterior of parallel lines and opposite side of transversal are congruent.

[tex]6x-35=4x+11[/tex] (Alternate exterior angles)

Now we will get two equations as:

[tex]6x-35+k=180[/tex] (Linear pair)

[tex]4x+11+k=180[/tex]

Now we will use substitution property to solve for k.

[tex]x=\frac{180-k+35}{6}[/tex]

[tex]4*(\frac{180-k+35}{6} )+11+k=180[/tex]

[tex]360-2k+70+33+3k=540[/tex]

[tex]k=540-463=77[/tex]

Therefore, measure of angle K is 77 degrees.