Question

1. (mangle lmj=x + 28), (mangle jmn=x + 124), and (mangle lmn = 144^{circ}). find (mangle jmn).

4)
classify each angle as acute, obtuse, right, or straight.

1. a) obtuse b) straight c) acute d) right
2. a) straight b) obtuse c) acute d) right

Explanation:

Step1: Analyze angle - sum relationship for $\angle LMN$

Given $m\angle LMJ=x + 28$, $m\angle JMN=x + 124$ and $m\angle LMN = 144$. Since $\angle LMN=\angle LMJ+\angle JMN$, we have the equation $(x + 28)+(x + 124)=144$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+x+28 + 124=2x+152$. So the equation becomes $2x+152 = 144$.

Step3: Solve for $x$

Subtract 152 from both sides: $2x=144−152=-8$. Then divide both sides by 2: $x=\frac{-8}{2}=-4$.

Step4: Find $m\angle JMN$

Substitute $x = - 4$ into the expression for $m\angle JMN$: $m\angle JMN=x + 124=-4+124 = 120$.

Step5: Classify the angle $\angle JMN$

Since an obtuse angle is an angle with measure greater than 90 degrees and less than 180 degrees, and $m\angle JMN = 120$ degrees, $\angle JMN$ is an obtuse angle.

For the multiple - choice part:

1. An angle that is greater than 90 degrees and less than 180 degrees is an obtuse angle. So the answer for 5) is A. obtuse.
2. (No information about angle in 6) is clear enough in the provided image to solve completely, but if we assume based on the options and general knowledge, an angle less than 90 degrees is acute. If the angle in 6) is less than 90 degrees, the answer would be C. acute).

Answer:

For the problem of finding $m\angle JMN$: 120
For 5): A. obtuse