Question

in a parallelogram,the measures of any two adjacent angles differ by 30°.find the measure of the angles of the parallelogram?

Answer 1

Solution :

Let the angle be x

The measures of any two adjacent angles differ by 30°

Total measures of  a parallelogram = 360°

According to the question

x + ( x + 30° ) + x + ( x + 30° ) = 360°

⇒ 4x + 60° = 360°

⇒ 4x = 360° - 60°

⇒ 4x = 300

⇒ x = 300/4

⇒ x = 75°

Find all angles

First Angle

x = 75°

Second Angle

⇒ x + 30°

⇒ 75° + 30°

⇒ 105°

Third Angle

⇒ 75°

Fourth Angle

⇒ x + 30°

⇒ 75° + 30°

⇒ 105°

Answer 2

Answer:

75°,105°,75°,15∆°

Step-by-step explanation:

solution-let the angle be x

the measure of any two adjacent angles differ by 30°

total measures of a parallelogram=360°

according to question

x+(x+30°)+x+(x+30°)=360°

4x+60°=360°

4x=360°-60°

4x=300°

x=75°

find all angles

first angle

x=75°

second angle

x+30°

75°+30°

105°

third angle750°

fourth angle

x+30°

75°+30°

105°

thanks