Question

find the missing angle measures:
angle 1 =
angle 2 =
angle 3 =
angle 4 =

Explanation:

Step1: Calculate ∠1 (supplementary to 92°)

$\angle 1 = 180^\circ - 92^\circ = 88^\circ$

Step2: Calculate ∠2 (supplementary to 123°)

$\angle 2 = 180^\circ - 123^\circ = 57^\circ$

Step3: Calculate ∠3 (triangle angle sum)

$\angle 3 = 180^\circ - \angle 1 - \angle 2 = 180^\circ - 88^\circ - 57^\circ = 35^\circ$

Step4: Calculate ∠4 (supplementary to ∠3)

$\angle 4 = 180^\circ - \angle 3 = 180^\circ - 35^\circ = 145^\circ$

Answer:

Angle 1 = $88^\circ$
Angle 2 = $57^\circ$
Angle 3 = $35^\circ$
Angle 4 = $145^\circ$