Question

what is the value of ( mangle dae ) and ( mangle dac )?
( circ ) ( mangle dae = 45^circ ) and ( mangle dac = 135^circ )
( circ ) ( mangle dae = 35^circ ) and ( mangle dac = 145^circ )
( circ ) ( mangle dae = 45^circ ) and ( mangle dac = 45^circ )
( circ ) ( mangle dae = 135^circ ) and ( mangle dac = 45^circ )
(12x - 3)(^circ) (10x + 5)(^circ)

Explanation:

Step1: Set equal vertical angles

$12x - 3 = 10x + 5$

Step2: Solve for x

$12x - 10x = 5 + 3$
$2x = 8$
$x = 4$

Step3: Calculate $m\angle DAE$

$m\angle DAE = 12x - 3 = 12(4) - 3 = 45^\circ$

Step4: Calculate $m\angle DAC$

$\text{Supplementary angles sum to }180^\circ$
$m\angle DAC = 180^\circ - 45^\circ = 135^\circ$

Answer:

$m\angle DAE = 45^\circ$ and $m\angle DAC = 135^\circ$ (the first option)