Question

7. In the adjoining figure, ABCD is a parallelogram. Find the values of x,y and z
PLS NEDFULLL HELP...... WITH NEAT EXPLANATION BECAUSE I AM LEARNING THIS FOR FIRST TIME .... MY FRIENDS PLSSSS​

Answer 1

given, ABCD is a parallelogram

angle B + angle C = 180° (sum of two adjacent angles)

40 + z + 105 = 180

z + 145 = 180

z = 180 - 145

z = 35°

< ADB = < DBC. (alternate interior angles)

< ADB = z = 35°

now

y + < ADB = 180° (linear pair)

y + 35 = 180

y = 180 - 35

y = 145°

now

AD = BC (opposite sides of a parallelogram)

2x + 3 = 3x + 1

3x - 2x = 3 - 1

x = 2

Answer 2

Given:

• AD = 2x+3cm
• BC = 3x+1cm
• $\angle$ DBA = 40°
• $\angle$ DCB = 105°

Find:

• Values of x,y and z will be ?

Solution:

we, know that

Opposite Sides of an paralleogram are equals

So,

$\sf \to AD =BC$

where,

• AD = 2x+3cm
• BC = 3x+1cm

Now,

$\sf \to 2x + 3 = 3x + 1$

Collect Like Terms

$\sf \to 2x - 3x = 1 - 3$

$\sf \to - x= - 2$

$\sf \to \cancel- x= \cancel - 2$

$\underline{ \boxed{ \color{indigo}\sf \to x= 2 \degree}}$

Now,

we, know that

If two lines are cut by an transversal line than the pair of an alternate angles are equals.

So, these are alternate exterior angles

$\angle$DBA = y = 40°

$\underline{ \boxed{ \color{aqua}\sf \to y= 40 \degree}}$

Now,

Again, If two lines are cut by an transversal line than the pair of an alternate angles are equals.

So, these are Alternate interior angles

$\angle$ABD= $\angle$CDB = 40°

Hence, $\angle$CDB = 40°

Now,

In triangle BCD

we, know that the sum of all angles of an triangle was 180° by angle sum property

So,

$\sf \to \angle CDB + \angle DBC + \angle DCB = 180 \degree$

where,

$\sf \bullet \angle CDB = 40 \degree \\ \sf \bullet \angle DBC = z \\ \sf \bullet \angle DCB = 105 \degree$

So,

$\sf \to 40 \degree + z + 105 \degree= 180 \degree$

$\sf \to z + 145 \degree= 180 \degree$

$\sf \to z = 180 \degree - 145 \degree = 35 \degree$

$\underline{ \boxed{ \color{red}\sf \to z= 35 \degree}}$

Hence, the value of

• x = 2°
• y = 40°
• z = 35°