Given: m is parallel to n; angle 1 and angle 2 are congruent; angle three and angle four are congruent. Prove angle 2 and angle 3 are complementary

Question

Given: m is parallel to n; angle 1 and angle 2 are congruent; angle three and angle four are congruent. Prove angle 2 and angle 3 are complementary

Answer 1

AB =N

CD=M

M || N

AB || CD

angle A = angle D

A=D

B= C

A+B+C+D = 360

A+D + B+C =360

A+A + B+B = 360

2A + 2B = 360

divide by 2

A + B = 180

A amd B are supplementary

D and C are supplementary

let A = angle 1 and B= angle 2

C= angle 3

D= angle 4

(odds are you or the problem meant supplementary, not complementary)

It's a parallelogram where adjacent angles are supplementary

if it really meant complementary there must be more information, a diagram or some verbal or written info that got left out

if two angles of a parallelogram are complementary they sum to 90 degrees

they would be opposite angles

the other two opposite angles would sum to 360-90 = 270 degrees

the 4 angles of a quadralateral such as a parallelogram sum to 360

if two angles are complementary, they each are 45

and the other 2 angles are each 270/2 = 135

then any 2 adjacent angles would sum to 45+135 = 180 and would be supplementary

if any 2 angles are supplementary it's a square