Chapter 5: Q1 (page 168)
Quadrilateral 
is a parallelogram.
- Why is
supplementary to 
? - Why is
supplementary to 
? - Complete: consecutive angles of a parallelogram are ?, while opposite angles are?.
Short Answer
is supplementary to 
because these are the adjacent angles on the same side of a transversal and therefore their sum is 
.
is supplementary to 
because these are the adjacent angles on the same side of a transversal and therefore their sum is
.- Consecutive angles of a parallelogram are supplementary, while opposite angles are congruent.
Step by step solution
Step 1. Observe the diagram.
The given diagram is:
Step 2. Description of step.
It is being given that 
is a parallelogram.
Therefore, 
and 
As, 
and 
is a transversal and the angles 
and 
are the adjacent angles on the same side of a transversal.
Therefore, the sum of the angles 
and 
is 
.
Therefore, 
is supplementary to 
.
Step 3. Description of step.
Therefore, 
is supplementary to 
because these are the adjacent angles on the same side of a transversal and therefore their sum is 
.
Step 1. Observe the diagram.
The given diagram is:
Step 2. Description of step.
It is being given that 
is a parallelogram.
Therefore, 
and 
.
As, 
and 
is a transversal and the angles 
and 
are the adjacent angles on the same side of a transversal.
Therefore, the sum of the angles 
and 
is 
.
Therefore, 
is supplementary to 
.
Step 3. Description of step.
Therefore, 
is supplementary to 
because these are the adjacent angles on the same side of a transversal and therefore their sum is 
.
Step 1. Observe the diagram.
The given diagram is:
Step 2. Description of step.
In the parallelogram the sum of the adjacent angles is 
and the opposite angles have the same measure.
Therefore, in parallelogram consecutive angles of a parallelogram are supplementary and opposite angles are congruent.
Step 3. Write the complete step.
Consecutive angles of a parallelogram are supplementary, while opposite angles are congruent.
