of interior angl ploring the interior angles of a triangle reset drag a vertex of the triangle to change its shape. double-click or double-tap a vertex or side to prevent it from changing. ∠c = 41° ∠a = 49° 8.0 ∠b = 90° create different examples of triangles. ∠c is represented by the purple section on line p. when m∠c increases, what happens to the middle section on line p? when m∠c decreases, what happens to the middle section on line p? it increases. it also decreases. it stays the same.

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Accepted Answer

# Explanation:
## Step1: Recall Triangle Angle Sum
The sum of interior angles in a triangle is $180^\circ$, so $m\angle A + m\angle B + m\angle C = 180^\circ$. The middle section on line $p$ relates to the other two angles (since the total on the straight line or the angle representation should sum appropriately, likely the sum of $\angle A$ and $\angle B$ or a related total).
## Step2: Analyze $m\angle C$ Increase
If $m\angle C$ increases, since the total of all three angles is fixed at $180^\circ$, the sum of $m\angle A + m\angle B$ must decrease. The middle section (related to the sum of the other two angles) will decrease.
## Step3: Analyze $m\angle C$ Decrease
If $m\angle C$ decreases, the sum of $m\angle A + m\angle B$ must increase (to keep the total $180^\circ$). Wait, no—wait, the middle section: looking at the diagram, the three angle sections (green, purple, red) on line $p$ should sum to a straight angle (or related fixed total, like $180^\circ$ as triangle angles). So if $\angle C$ (purple) increases, the middle (say, related to the other two angles) must decrease. If $\angle C$ decreases, the middle (sum of other two) increases? Wait, no, the options for the second part: when $m\angle C$ decreases, what happens to middle? Wait, the first question: when $m\angle C$ increases, middle section (let's say the non - purple, non - red? Wait, the diagram has three sections: green, purple ($\angle C$), red. So total of the three angles (as they are on a straight line, maybe) should be $180^\circ$ (like the triangle's angle sum). So if $\angle C$ (purple) increases, the sum of green and red (middle? Wait, maybe the middle is the red? No, the first question: "when $m\angle C$ increases, what happens to the middle section on line $p$?" Let's re - think. The triangle's angles: $\angle A$, $\angle B$, $\angle C$ sum to $180^\circ$. The sections on line $p$ represent these angles. So if $\angle C$ (purple) increases, then the sum of $\angle A$ and $\angle B$ (the other two sections) must decrease. So the middle section (assuming middle is one of the other two, or the sum) – but the options for the second part (when $m\angle C$ decreases) has options: increases, decreases, stays same. Wait, the key is the sum of angles in a triangle is constant ($180^\circ$). So if $\angle C$ increases, the sum of $\angle A$ and $\angle B$ decreases. So the middle section (if it's related to $\angle A$ or $\angle B$ or their sum) – when $m\angle C$ increases, the middle section (say, the one related to the sum of the other two) decreases. When $m\angle C$ decreases, the sum of the other two increases, so the middle section increases? Wait, no, the second question's options: when $m\angle C$ decreases, what happens to middle? The options are "It increases", "It also decreases", "It stays the same". Wait, maybe the middle section is the one that is not $\angle C$ and not the right - most (red, maybe $\angle B$). Wait, the triangle has $\angle B = 90^\circ$ in the example. Wait, maybe the three sections on line $p$ are $\angle A$ (green), $\angle C$ (purple), $\angle B$ (red), and they sum to $180^\circ$ (since triangle angles sum to $180^\circ$). So if $\angle C$ (purple) increases, then $\angle A+\angle B$ (green + red) must decrease. So the middle section (if middle is red, or green, or their sum) – but the first question: when $m\angle C$ increases, middle section (let's say the red one, $\angle B$) – no, $\angle B$ could be right angle. Wait, maybe the middle section is the one between green and red, but no. Let's focus on the angle sum. Since $\angle A+\angle B+\angle C = 180^\circ$, if $\angle C$ increases, $\angle A+\angle B$ decreases. So the section(s) representing $\angle A$ and $\angle B$ (the middle - related) will decrease. When $\angle C$ decreases, $\angle A+\angle B$ increases, so the middle section (representing $\angle A+\angle B$) will increase. But the options for the second part: when $m\angle C$ decreases, what happens to middle? The options are "It increases", "It also decreases", "It stays the same". So for the first blank (when $m\angle C$ increases, middle section): it decreases. For the second blank (when $m\angle C$ decreases, middle section): it increases. But let's check the options. Wait, the first question's dropdown: let's assume the middle section is related to the sum of the other two angles. So when $m\angle C$ increases, the middle section (sum of $\angle A$ and $\angle B$) decreases. When $m\angle C$ decreases, the middle section (sum of $\angle A$ and $\angle B$) increases.

# Answer:
First question (when $m\angle C$ increases): It decreases.
Second question (when $m\angle C$ decreases): It increases.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall Triangle Angle Sum

Step2: Analyze \(m\angle C\) Increase

Step3: Analyze \(m\angle C\) Decrease

Answer: