Question

question 1.17
∠j and ∠k form a linear - pair. twice the measure of ∠k is 48° more than the measure of ∠j. what is the measure of each angle? select all that apply
□ m∠j = 104°
□ m∠j = 44°
□ m∠j = 76°
□ m∠k = 76°
□ m∠k = 136°
□ m∠k = 104°

Explanation:

Step1: Set up equations

Since $\angle J$ and $\angle K$ form a linear - pair, $\angle J+\angle K = 180^{\circ}$, so $\angle J=180 - \angle K$. Also, $2\angle K=\angle J + 48^{\circ}$.

Step2: Substitute $\angle J$ in the second equation

Substitute $\angle J = 180-\angle K$ into $2\angle K=\angle J + 48^{\circ}$, we get $2\angle K=(180 - \angle K)+48^{\circ}$.

Step3: Solve for $\angle K$

Expand the right - hand side: $2\angle K=180^{\circ}-\angle K + 48^{\circ}$. Combine like terms: $2\angle K+\angle K=180^{\circ}+48^{\circ}$, $3\angle K = 228^{\circ}$. Then $\angle K=\frac{228^{\circ}}{3}=76^{\circ}$.

Step4: Solve for $\angle J$

Since $\angle J+\angle K = 180^{\circ}$, then $\angle J=180^{\circ}-\angle K$. Substitute $\angle K = 76^{\circ}$, we get $\angle J=180^{\circ}-76^{\circ}=104^{\circ}$.

Answer:

A. $m\angle J = 104^{\circ}$
D. $m\angle K = 76^{\circ}$