The measure of ∠1 is 95°
Solution:
Given a || b.
m∠6 = 85° and m∠3 = 2x°
∠6 and ∠3 are co-interior angles.
Co-interior angles add up to 180°.
⇒ m∠6 + m∠3 = 180°
⇒ 85° + 2x° = 180°
Subtract 85° from both sides.
⇒ 2x° = 95°
⇒ m∠3 = 95°
If two lines cut each other, then vertically opposite angles are congruent.
⇒ m∠1 = m∠3
⇒ m∠1 = 95°
Hence the measure of ∠1 is 95°.
