in triangle rst, the measure of angle r is 39, the measure of angle s is x, and the measure of angle t is…

in triangle rst, the measure of angle r is 39, the measure of angle s is x, and the measure of angle t is (5x - 3). point l lies on rs, point k lies on st, and lk is parallel to rt. what is the measure, in degrees, of angle skl? (disregard the degree symbol when entering your answer)

in triangle rst, the measure of angle r is 39, the measure of angle s is x, and the measure of angle t is (5x - 3). point l lies on rs, point k lies on st, and lk is parallel to rt. what is the measure, in degrees, of angle skl? (disregard the degree symbol when entering your answer)

Answer

Explanation:

Step1: Use angle - sum property of a triangle

In (\triangle RST), the sum of interior angles is (180^{\circ}), so (39 + x+(5x - 3)=180).

Step2: Simplify the left - hand side of the equation

Combine like terms: (39+x + 5x-3=180), which simplifies to (6x + 36=180).

Step3: Solve for (x)

Subtract 36 from both sides: (6x=180 - 36=144). Then divide both sides by 6, so (x = 24).

Step4: Use the property of parallel lines

Since (LK\parallel RT), (\angle SKL) and (\angle T) are corresponding angles. So (\angle SKL=\angle T). Substitute (x = 24) into the expression for (\angle T), (\angle T=5x-3=5\times24 - 3=120 - 3=117).

Answer:

117