1. The first question is about adjusting areas in sections, but without numerical data or a table, we cannot determine the best fix. Please provide the table or data for analysis.
2. Problem: In triangle $\triangle ABC$, angles $\angle A$ and $\angle C$ are congruent, and $\angle B = 143.6^\circ$. Find the measure of $\angle A$.
Step 1. Recall that the sum of interior angles in any triangle is $180^\circ$.
Step 2. Since $\angle A$ and $\angle C$ are congruent, let $\angle A = \angle C = x$.
Step 3. Write the equation for the sum of angles:
$$x + 143.6 + x = 180$$
Step 4. Simplify:
$$2x + 143.6 = 180$$
Step 5. Subtract $143.6$ from both sides:
$$2x + \cancel{143.6} - \cancel{143.6} = 180 - 143.6$$
$$2x = 36.4$$
Step 6. Divide both sides by 2:
$$\frac{2x}{\cancel{2}} = \frac{36.4}{\cancel{2}}$$
$$x = 18.2$$
Answer: $\angle A = 18.2^\circ$, which corresponds to option F.
3. Problem: Factor the quadratic expression $x^2 - x - 30$.
Step 1. We look for two numbers that multiply to $-30$ and add to $-1$ (the coefficient of $x$).
Step 2. The pairs of factors of 30 are (1,30), (2,15), (3,10), (5,6).
Step 3. Check which pair can sum to $-1$ when one is negative:
- $5$ and $-6$ sum to $-1$.
Step 4. So, factorization is:
$$(x - 6)(x + 5)$$
Answer: Option C.
Final answers:
- Question 4: $18.2^\circ$ (F)
- Question 5: $(x - 6)(x + 5)$ (C)
Triangle Angles Factoring 1F7384
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