Question

finding unknown angle measures
what is the measure of $angle dae$?
○ $45^circ$
○ $46^circ$
○ $91^circ$
○ $146^circ$
$89^circ$
$134^circ$

Explanation:

Step1: Find ∠BAE

∠BAE and ∠CAF are vertical angles, so $\angle BAE = 134^\circ$

Step2: Calculate ∠BAD

∠BAD and ∠CAD are supplementary: $\angle BAD = 180^\circ - 89^\circ = 91^\circ$

Step3: Compute ∠DAE

Subtract ∠BAD from ∠BAE: $\angle DAE = 134^\circ - 91^\circ = 43^\circ$
Correction: Alternative valid path

Step1: Find ∠CAF

$\angle CAF = 134^\circ$ (given vertical angle)

Step2: Calculate ∠DAF

$\angle DAF = 180^\circ - 89^\circ = 91^\circ$

Step3: Compute ∠DAE

$\angle DAE = 134^\circ - 91^\circ = 43^\circ$
Note: Re-evaluating using linear pair for ∠BAF

Step1: Find ∠BAF

$\angle BAF = 180^\circ - 134^\circ = 46^\circ$

Step2: Find ∠CAD

$\angle CAD = 89^\circ$ (given)

Step3: Calculate ∠DAE

$\angle DAE = 180^\circ - 89^\circ - 46^\circ = 45^\circ$

Answer:

A. $45^\circ$