Question

two adjacent angles of a parrellelogram are of measure (2x-3) and (3x-7).find the measures

Answer 1

●We know that co-interior angles of a parallelogram are supplementary.

●So,

(2x-3)+(3x-7) = 180°.
2x-3+3x-7 = 180.
5x - 10 = 180.
5x = 180+10.
5x = 190.
x = 190/5.
x = 38.

○ (2x-3) = [2(38)-3] = (76-3) = 73°.
○ (3x-7) = [3(38)-7] = (114-7) = 107°.


★Therefore, the measure of the angles of the parallelogram are 73°, 107°, 73° and 107°.

Answer 2

Hello!

Since,
Co-interior angles of a parallelogram are $\underline{\sf supplementary}$.

(2x - 3) + (3x - 7) = 180°

⇒ 2x - 3 + 3x - 7 = 180°

⇒ 5x - 10 = 180.

⇒ 5x = 180 + 10

⇒ 5x = 190.

⇒ x = $\dfrac{\sf 190}{\sf 5}$ = $\boxed{\sf x = 38}$

Hence,
The measures of original angles are :-

• (3x-7) = 3(38) - 7 = (114 - 7) = $\bf{107^{\circ}}$
• (2x - 3) = 2(38) - 3 = (76 - 3) = $\bf{73^{\circ}}$

Cheers!