Given angle K is supplementary to angle J angle L is supplem

Given: angle K is supplementary to angle J. angle L is supplementary to angle J. Which of these statements must be true? A. angle K is adjacent to angle L. B. angle K is congruent to angle L. C. angle K is supplementary to angle L. D. angle K is complementary to angle L.

Solution

B is right. Please have a look at the detailed solution. Leave a comment in case you don\'t understand any part of it.

K is supplementry to J.
L is summplmentry to J

Supplementery angle definition - either of two angles whose sum is 180°.

So, K+J = 180....1
So, L+J = 180.....2

K and L therefore will never sum to 180, hence K and L aren\'t supplemtrey, therefore C is out.

A is out as they may not be adjucent,

D is also out, as they may not sum to 90 ( complementry angles) [please note that the questions asks for \'Must\' right answer]

From equations 1 and 2...we get....K+J = L+J = 180.

Hence, K= L

which can only happen when K and L are congruent.

So, B is right.