The difference in the measure of two supplementary angles is 84. Find the angles.
7. ABCD is a parallelogram find the angle measures x and y:
state the properties used to find them.
Answers
Question :-
1) The difference in the measure of two supplementary angles is 84. Find the angles.
2) ABCD is a parallelogram. Find the angle measures x and y. State the properties used to find them.
Answer :-
1) Let the angle be x
Supplementary angle = 180 - x
According to the question :-
↬ x - ( 180 - x ) = 84
↬ x + x - 180 = 84
↬ 2x = 180 + 84
↬ 2x = 264
↬ x = 264/2
↬ x = 132
Supplementary angle = 180 - 132 = 48
Angles = 132° and 48°
2) ∠ ABC + 80° = 180° ( linear pair )
↬ ∠ABC = 180° - 80°
↬ ∠ABC = 100°
We know that,
Opposite angles of parallelogram are equal.
So,
↬ ∠ABC = ∠ADC
↬ y = ∠ADC
↬ y = 100°
Also,
Adjacent angles of the parallelogram sums upto 180°.
↬ ∠ABC + ∠BAD = 180°
↬ 100 + 30 + x = 180
↬ x + 130 = 180
↬ x = 180 - 130
↬ x = 50°
Answer:
Supplementary angle = 180 - 132 = 48
Step-by-step explanation:
Q. The difference in the measure of two supplementary angles is 84. Find the angles.
Let the angle be x
Supplementary angle = 180 - x
According to the question :-
x - ( 180 - x ) = 84
x + x - 180 = 84
2x = 180 + 84
2x = 264
x = 264/2
x = 132
Supplementary angle = 180 - 132 = 48