Question

nd the value of the variables in the figure. a (4y + 3)° (5x - 7)° (3x + 17)° b

Explanation:

Step1: Find the value of \( x \)

Since \( (5x - 7)^{\circ} \) and \( (3x + 17)^{\circ} \) are alternate - interior angles (lines \( a\parallel b \)), we have the equation \( 5x-7 = 3x + 17 \).
Subtract \( 3x \) from both sides: \( 5x-3x-7=3x - 3x+17 \), which simplifies to \( 2x-7 = 17 \).
Add \( 7 \) to both sides: \( 2x-7 + 7=17 + 7 \), so \( 2x=24 \).
Divide both sides by \( 2 \): \( x=\frac{24}{2}=12 \).

Step2: Find the value of \( y \)

Since \( (5x - 7)^{\circ} \) and \( (4y + 3)^{\circ} \) are supplementary angles (they form a linear pair), when \( x = 12 \), \( 5x-7=5\times12-7=60 - 7 = 53^{\circ} \).
Then \( 53+(4y + 3)=180 \).
Simplify the left - hand side: \( 4y+56 = 180 \).
Subtract \( 56 \) from both sides: \( 4y+56-56=180 - 56 \), so \( 4y=124 \).
Divide both sides by \( 4 \): \( y=\frac{124}{4}=31 \).

Answer:

\( x = 12,y = 31 \)