Question

5. The opposite angles of a parallelogram are ( 3x+5)° and (61-x)". Find the
measure of four angles.​

Answer 1

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

In a Parallelogram, opposite angles are equal

In the above figure, ∠ADC = ∠ABC

⇒ (3x + 5)° = (61 - x)°

⇒ 3x + 5 = 61 - x

⇒ 3x + x = 61 - 5

⇒ 4x = 56

⇒ x = 56 ÷ 4

⇒ x = 14

∠ADC = ∠ABC

= (3x + 5)°

= 3(14) + 5

= 47°

∴ ∠ADC = ∠ABC = 47°

In a Parallelogram, adjacent angles sum up to 180°

∠DCB = ∠DAB

= 180 - 47

= 133°

∴ ∠DCB = ∠DAB = 133°