Question

Find the value of x and the
measure of all the angles in
the given parallelogram.
​

Answer 1

$\color{grey} \cal \huge \underline { \underline{ANSWER}}$

As we know that opposite angles of a parellelogram are always equal so we can write:

$\LARGE\sf 3x-5°=2x+35°$

$\LARGE\sf 3x-2x=35°+5°$

$\LARGE \boxed{ \color{seagreen} \sf x=40°}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\LARGE \sf\angle D = x - 5 \degree$

$\LARGE \sf\angle D = 40 \degree - 5 \degree$

$\LARGE \sf\angle D = 35 \degree$

$\LARGE \sf \red{\angle D = \angle B = 35 \degree}$

$\blue{ \sf[Opposite \: Angle \: of \: ||gm]}$

$\LARGE\sf \angle D+ \angle A=180°$

$\blue{ \sf[Adjacent \: angles \: of \: ||gm]}$

$\LARGE\sf 35 \degree+ \angle A=180°$

$\LARGE\sf \angle A=180° - 35 \degree$

$\LARGE\sf {\angle A=145° }$

$\LARGE\sf \red{ \angle A= \angle C=145°}$

$\blue{ \sf[Opposite \: Angle \: of \: ||gm]}$

$\large \sf So \: angles \: of \: ||gm \: are:-$

$\sf \LARGE \pink{\angle A=145°}$

$\sf \LARGE \green{ \angle B=35°}$

$\sf \LARGE \orange{ \angle C=145°}$

$\sf \LARGE \color{blue}\angle D=35°$

Answer 2

Answer:

Angles A and C = 65°

Angles D and B = 115°

Step-by-step explanation:

As we know, opposite angles of a parallelogram are equal, we can say

(3x - 5)° = (2x + 35)°

3x - 2x = 35° + 5°

x = 40°

Angle D = 40° × 3 = 120° - 5° = 115°

Using the property adjacent angles sum up to 180°, we can say

Angles A & C = 180° - 115° = 65°

Hope it helps.