1 Answer

Colin Armstrong · Answer 1 · 2023-08-01T14:17:28+0000

Angle (6x + 1) and Angle (2x + 17) is a pair of Alternate Interior Angles.

Under the Alternate Interior Angles Theorem, it states that a pair of Alternate Interior Angles are always congruent.

Thus, we can say that (6x + 1) = (2x + 17). Let's now solve for x.

$\text{ (6x + 1)}^(\circ)=(2x+17)^(\circ)$
$\text{ 6x - 2x = 17 - 1}$
$\text{ 4x = 16 ; x = }(16)/(4)$
$\text{ x = 4}$

Angle (2x + 17) and y are Supplementary Angles. This means that the measure of Angle (2x + 17) and y when added up equal to 180 degrees.

Thus, we make this equation to solve for y, given that x = 4.

$\text{ (2x + 17)}^(\circ)+y=180^(\circ)$
$\text{ 2(4) + 17 + y = 180}$
$8\text{ + 17 + y = 180 ; 25 + y = 180}$

$25\text{ + y - 25 = 180 - 25}$
$\text{ y = 155 = 155}^(\circ)$

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