. Two consecutive angles of a parallelogram measure (10x+30) and (6x+38)",
respectively. What are the ineasures of these angles?
A 90° and 90°
B. 110 and 70°
C100 and 80
D 150° and 30°
Answers
Option C
Step-by-step explanation:
Given:-
Two consecutive angles of a parallelogram measure (10x+30)° and (6x+38)°
To find:-
What are the measurements of the angles?
Solution:-
Given that:
Two consecutive angles of a parallelogram measure (10x+30)° and (6x+38)°
We know that
The sum of adjacent angles in a Parallelogram is 180°
=> (10x+30)° + (6x+38)° = 180°
=> (10x+6x) +(30°+38°) = 180°
=> 16x + 68° = 180°
=> 16x = 180° - 68°
=> 16x = 112°
=> x = 112°/16
=> x = 7°
Now,
10x +30°
=> 10×7° +30°
=> 70°+30°
=>100°
and 6x+38°
=> 6×7°+38°
=> 42°+38°
=> 80°
The angles are 100° and 80°
Answer:-
The measurements of the Consecutive angles are 100° and 80°
Used formula:-
- The adjacent angles in a Parallelogram are Supplementary.
Given :-
- Two consecutive angles of a parallelogram measure ( 10x + 30 ) and ( 6x + 38) respectively.
To Find :-
- What are the measures of these angles?
Solution :-
~Here, we’re given the variable values of consecutive angles of a parallelogram and we need to find measure of each angle. We can form an equation according to the given values and we know that consecutive angles of a parallelogram are supplementary. By solving that equation we can find the measure of each angle.
_____________
As we know that ,
★ According to the supplementary angle property , sum of two angles is 180°.
According to the question :-
⟶ ( 10x + 30 ) + ( 6x + 38 ) = 180
⟶ 16x + 68 = 180
⟶ 16x = 112
⟶ x = 112/16
⟶ x = 7
Finding the angles :-
- First angle = ( 10x + 30 )
→ 10 × 7 + 30
→ 70 + 30
→ 100 °
- Second angle = ( 6x + 38 )
→ 6 × 7 + 38
→ 42 + 38
→ 80 °
_____________
Hence,
- Measures of these angles are 100° and 80° ( Option c )