Question

1. in the quadrilateral jkse, angles are given as: at j: 127°, at k: (10x + 7)°, at s: 88°, at e: (5x + 3)°. (the figure shows quadrilateral jkse with vertices j, k, s, e and angle markings as described.)

Explanation:

Step1: Use the formula for the sum of interior angles of a quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\). So, \((5x + 3)+127+(10x + 7)+88 = 360\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((5x+10x)+(3 + 127+7+88)=15x+(130 + 95)=15x + 225\).
The equation becomes \(15x+225 = 360\).

Step3: Solve for \(x\)

Subtract 225 from both sides: \(15x=360 - 225\), so \(15x = 135\).
Divide both sides by 15: \(x=\frac{135}{15}=9\).

Answer:

\(x = 9\)