Question

1. find the $m\angle ule$ in the triangle below.

Explanation:

Step1: Find ∠RUL's adjacent angle

∠RUL and ∠LUE are supplementary, so:
$m\angle LUE = 180^\circ - 109^\circ = 71^\circ$

Step2: Calculate m∠ULE

Use triangle angle sum ($180^\circ$):
$m\angle ULE = 180^\circ - m\angle LUE - m\angle E$
$m\angle ULE = 180^\circ - 71^\circ - 49^\circ$

Answer:

$60^\circ$