Question

find the measure of the angle indicated in bold. 85° 7° 4° 110°

Explanation:

Step1: Set up equation

Since the two angles are equal (assuming they are corresponding or alternate - interior/exterior angles), we set up the equation $20x + 5=24x−1$.

Step2: Solve for x

Subtract $20x$ from both sides: $5 = 4x−1$. Then add 1 to both sides: $6 = 4x$. Divide both sides by 4: $x=\frac{6}{4}=\frac{3}{2}$.

Step3: Find angle measure

Substitute $x = \frac{3}{2}$ into $20x + 5$. So, $20\times\frac{3}{2}+5=30 + 5=35$. But this is wrong. Let's assume the two angles are supplementary, so $20x+5+24x - 1=180$.

Step4: Combine like - terms

$(20x+24x)+(5 - 1)=180$, which gives $44x+4 = 180$.

Step5: Isolate x

Subtract 4 from both sides: $44x=176$. Divide both sides by 44: $x = 4$.

Step6: Find angle measure

Substitute $x = 4$ into $20x+5$. We get $20\times4+5=80 + 5=85$.

Answer:

$85^{\circ}$