Question

question 1 - 13
∠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 based on given info

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

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

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

Step3: Solve the equation for $m\angle K$

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

Step4: Solve for $m\angle J$

Substitute $m\angle K = 76^{\circ}$ into $m\angle J = 180 - m\angle K$, we get $m\angle J=180 - 76=104^{\circ}$.

Answer:

C. $m\angle J = 76^{\circ}$, F. $m\angle K = 104^{\circ}$