Question

what are the values of a and b?
a =
b =
submit

Explanation:

Step1: Use exterior angle theorem

The exterior angle $a$ equals the sum of the two remote interior angles:
$a = (a-31^\circ) + (a-32^\circ)$

Step2: Simplify and solve for $a$

Expand and rearrange the equation:
$a = 2a - 63^\circ$
$2a - a = 63^\circ$
$a = 63^\circ$

Step3: Use linear pair for $b$

Angles $a$ and $b$ are supplementary:
$a + b = 180^\circ$

Step4: Substitute $a$ to find $b$

$63^\circ + b = 180^\circ$
$b = 180^\circ - 63^\circ = 117^\circ$

Answer:

$a = 63^\circ$
$b = 117^\circ$