Question

1. a pair of same side exterior angles are 13a and 10b. a pair of alternate interior angles are 5a and 10b. find the value of a and b.

Explanation:

Step1: Use alternate - interior angles property

Since alternate - interior angles are equal, we have $5a = 10b$. Simplify this equation:
$a = 2b$.

Step2: Use same - side exterior angles property

Same - side exterior angles are supplementary, so $13a+10b = 180$.
Substitute $a = 2b$ into $13a + 10b=180$:
$13\times(2b)+10b = 180$.
$26b+10b = 180$.
$36b = 180$.
Solve for $b$: $b=\frac{180}{36}=5$.

Step3: Find the value of $a$

Substitute $b = 5$ into $a = 2b$.
$a=2\times5 = 10$.

Answer:

$a = 10$, $b = 5$