Question

the two opposite angles of a parallelogram are (3y-10) and (2y+35). find the measures of all the four angles of the parallelogram.​

Answer 1

Step-by-step explanation:

(3y-10)=(2y+35) (opposite angles are

equal

3y-2y=35+10

y=45

3y-10=(3x36)-10

=135-10

=125°

2y+35=125°(opposite angles are equal)

Angle1=180°-125°(adjacent angles are

=55° Supplementary)

Angle2=55°(opposite angles are equal)

Answer 2

The measures of all the four angles of the parallelogram are 55° , 125° , 55° and 125° if two opposite angles of a parallelogram are (3y-10) and (2y+35)

Given:

• The two opposite angles of a parallelogram are (3y-10) and (2y+35)

To Find:

• The measures of all the four angles of the parallelogram.​

Solution:

• Measures of opposite angles of a parallelogram are equal
• Adjacent angles of a parallelogram are supplementary hence adds up to 180°

Step 1:

Equate opposite angles (3y-10) and (2y+35)

3y - 10  = 2y + 35

Step 2:

Solve for y

3y - 10  = 2y + 35

3y - 2y = 35 + 10

=> y = 45

Step 3:

Substitute y = 45  in 3y - 10

3(45) - 10  = 125

Hence these two opposite angles are 125°

Step 4:

Subtract 125 from 180 to find remaining two angles

180° - 125° = 55°

The measures of all the four angles of the parallelogram are 55° , 125° , 55° and 125° if two opposite angles of a parallelogram are (3y-10) and (2y+35)