Subjects geometry, algebra

Triangle Angles Factoring 1F7384

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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)