Question

unit test review active 1 2 3 4 5 6 angle k measures 67° and angle l measures 119°. what are the measures of angles m and n? m ∠m = 61° and m ∠n = 113° m ∠m = 67° and m ∠n = 119° m ∠m = 113° and m ∠n = 61° m ∠m = 119° and m ∠n = 67°

Explanation:

Step1: Recall cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles are supplementary, meaning their sum is $180^\circ$.

Step2: Calculate $\angle M$

$\angle K$ and $\angle M$ are opposite angles.
$m\angle M = 180^\circ - m\angle K = 180^\circ - 67^\circ = 113^\circ$

Step3: Calculate $\angle N$

$\angle L$ and $\angle N$ are opposite angles.
$m\angle N = 180^\circ - m\angle L = 180^\circ - 119^\circ = 61^\circ$

Answer:

$m \angle M = 113^\circ$ and $m \angle N = 61^\circ$ (the third option)