Question

Please help it’s due today!!!

Answer 1

Answer:

(a.):  m∠ ACB = 40°; (b.):  m ∠CBA = 25°; (c.):  m ∠CAB = 115°

Step-by-step explanation:

Because Lines AB and DE are parallel, we can use the angle relationships to find the angles.

(For context of the problem, we can label the 40° angle as ∠C and the 155° as ∠B)

(a.) Angles C and ACB are vertical angles, which means they're congruent.  Thus m ∠ACB = 40°.

(b.) AB is a straight line and angles B and CBA are supplementary angles.  This means their total sum is 180°.  We need to subtract angle B from 180 to find m ∠CBA:

$180-155=CBA\\25=CBA$

(c.) We know that the sum of all the angles is 180°.  Thus, we can subtract the sum of angles CBA and CBA from 180 to find the m ∠CAB:

$180-(40+25)=CAB\\180-65=CAB\\115=CAB$