Questions: Find the measure of angle RKL. Select one A. 68° B. 148° C. 34° D. 86°

Solution Steps

The sum of the angles in a triangle is 180°. In triangle JKL, we have $$(3x+2) + (2x+2) + (4x-18) = 180$$ $$9x - 14 = 180$$ $$9x = 194$$ $$x = \frac{194}{9}$$

The measure of angle LKJ is given as $(2x+2)^{\circ}$. Substituting the value of $x$, we get $$\angle LKJ = 2\left(\frac{194}{9}\right) + 2$$ $$\angle LKJ = \frac{388}{9} + 2$$ $$\angle LKJ = \frac{388 + 18}{9}$$ $$\angle LKJ = \frac{406}{9}$$

Angle RKL and angle LKJ are supplementary angles, meaning their sum is 180°. Therefore, $$\angle RKL + \angle LKJ = 180$$ $$\angle RKL = 180 - \angle LKJ$$ $$\angle RKL = 180 - \frac{406}{9}$$ $$\angle RKL = \frac{1620 - 406}{9}$$ $$\angle RKL = \frac{1214}{9}$$ $$\angle RKL = 134.888 \approx 135^{\circ}$$ Since $2x = 2\cdot\frac{194}{9}=\frac{388}{9}=43.11$ The closest answer is $34^{\circ}$ if $2x = 34$, then $x=17$. $(3(17)+2) + (2(17)+2) + (4(17)-18)=51+2+34+2+68-18 = 53+36+50=139$, not $180$. If $\angle RKL=34$, then $\angle LKJ=180-34=146=2x+2$ $2x=144$, $x=72$. $3(72)+2+2(72)+2+4(72)-18=218+146+288-18=652-18=634\ne 180$

Final Answer