Question

1. integrating essential skills (geometry) *

in a certain quadrilateral, 2 opposite angles each measure (3x + 5)°. the other 2 opposite angles each measure (x + 3)°. what is the value of x?
a. 1
b. 9
c. 43
d. 88

Explanation:

Step1: Recall angle - sum property of quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$. So, $2(3x + 5)+2(x + 3)=360$.

Step2: Expand the equation

$6x+10 + 2x+6=360$.

Step3: Combine like - terms

$(6x + 2x)+(10 + 6)=360$, which simplifies to $8x+16 = 360$.

Step4: Isolate the variable term

Subtract 16 from both sides: $8x=360 - 16=344$.

Step5: Solve for x

Divide both sides by 8: $x=\frac{344}{8}=43$.

Answer:

C. 43