Find the angle measures. Justify your responses.

Given: a||b, m∠3=63

Find: m∠6,m∠7

m∠6 = 117°

m∠7 = 63°

Step-by-step explanation:

It's given that a║b and m∠3 = 63°

Since, ∠3 and ∠6 are the consecutive interior angles,

m∠3 + m∠6 = 180°

63° + m∠6 = 180°

m∠6 = 180° - 63°

        = 117°

Since, ∠3 and ∠7 are the corresponding angles,

Therefore, ∠3 ≅ ∠7

m∠7 = m∠3 = 63°

the arc length is found by finding the circumference of the full circle (2xpixradius) and then dividing by 4 to find just one quarter of the circle (90 degrees).