Question

if m∠4 = 35°, find m∠2 and m∠3
m∠2 =

m∠3 =

Explanation:

Step1: Identify angle - relationship for ∠2 and ∠4

∠2 and ∠4 are alternate - interior angles. For parallel lines AB and CD (assumed from the diagram), alternate - interior angles are equal.
$m\angle2=m\angle4$

Step2: Substitute the value of ∠4

Given $m\angle4 = 35^{\circ}$, so $m\angle2=35^{\circ}$

Step3: Identify angle - relationship for ∠3 and ∠4

∠3 and ∠4 are complementary angles since the angle formed at point C is a right - angle (indicated by the square symbol). So $m\angle3 + m\angle4=90^{\circ}$

Step4: Solve for ∠3

$m\angle3=90^{\circ}-m\angle4$. Substituting $m\angle4 = 35^{\circ}$, we get $m\angle3=90 - 35=55^{\circ}$

Answer:

$m\angle2 = 35^{\circ}$
$m\angle3 = 55^{\circ}$