Given the following diagram, find the required measure. given: m ∠3 = m ∠7 all of the following are true except a) m∠1 = m∠3 + m∠5 b) m∠5 = m∠4 + m∠7 c) m∠3 = m∠6 + m∠7 d) m∠1 = m∠5 + m∠7

Angle 3 is not an exterior angle to the triangle containing 6 and 7. The triangle containing 6 and 7 would have to have the supplement of 4 in the list. In fact, you have nothing in the diagram that shows anything resembling the supplement of 4. You could prove all the other statements using the given statement or just the sum of the remote interior angles = the exterior angle.

For example in D <1 = <3 + < 5 But by the given, <3 = <7 so

<1 = <5 + <7. That makes answer D true.

B is true because the exterior angle is equal to the 2 remote interior angles.

A is true because <1 = the sum of the two remote interior angles.