Question

. ∠JKL and ∠RST are complementary. m∠JKL = 36° and m∠RST = (x + 15)°. Find the value of x and the measure of ∠RST.

Answer 1

The value of x is 39 and the measure of angle RST is 54 degree.

Explanation:

It is given that the angle JKL and angle RST are complementary angle.

If two angle are complementary angles, then their sum must be 90 degree.

Since the angle JKL and angle RST are complementary angle, therefore

`\angle JKL+\angle RST=90^(\circ)`

`36^(\circ)+(x+15)^(\circ)=90^(\circ)`

`36^(\circ)+x^(\circ)+15^(\circ)=90^(\circ)`

`51^(\circ)+x^(\circ)=90^(\circ)`

`x^(\circ)=90^(\circ)-51^(\circ)`

`x^(\circ)=39^(\circ)`

Therefore the value of x is 39.

`\angle RST=(x+15)^(\circ)`

`\angle RST=(39+15)^(\circ)`

`\angle RST=54^(\circ)`

Therefore the measure of angle RST is 54 degree.