Question

1. iotp is an isosceles trapezoid. find the missing values.

a =
b =

Explanation:

Step1: Use same-side interior angles

Since $OT \parallel SR$, $\angle OTS$ and $\angle a$ are same-side interior angles, so they are supplementary.
$\angle a + 112^\circ = 180^\circ$
$\angle a = 180^\circ - 112^\circ = 68^\circ$

Step2: Use properties of isosceles trapezoid

In an isosceles trapezoid, base angles are equal, and $OT \parallel IP$. $\angle b$ is supplementary to $\angle a$ (same-side interior angles for $OS \parallel PR$).
$\angle b + \angle a = 180^\circ$
$\angle b = 180^\circ - 68^\circ = 112^\circ$
Alternatively, $\angle b$ is equal to $\angle O$ as base angles of the trapezoid.

Answer:

$a = 68$
$b = 112$