Question

5.4 assignment
possible points: 1.43
writing measurements in order list the sides and the angles in order from smallest to largest.
(image of triangle mnp with angle at n: 127°, angle at p: 29°)
sides (smallest to largest): blank, blank, blank
angles (smallest to largest): blank, blank, ∠n
options: mn, mp, np, ∠m, ∠p

Explanation:

Step1: Find the third angle

In a triangle, the sum of angles is $180^\circ$. Given $\angle N = 127^\circ$ and $\angle P = 29^\circ$, so $\angle M = 180 - 127 - 29 = 24^\circ$.

Step2: Order angles

Angles: $\angle M = 24^\circ$, $\angle P = 29^\circ$, $\angle N = 127^\circ$. So order (smallest to largest): $\angle M$, $\angle P$, $\angle N$.

Step3: Relate angles to sides (larger angle opposite longer side)

• $\angle M$ is opposite $NP$, $\angle P$ opposite $MN$, $\angle N$ opposite $MP$.
• Since $\angle M < \angle P < \angle N$, then sides opposite: $NP < MN < MP$.

Answer:

Sides (smallest to largest): $NP$, $MN$, $MP$
Angles (smallest to largest): $\angle M$, $\angle P$, $\angle N$