Question

Q4 MY SCHOOL HW BUT I CANT SOLVE PLZ FAST ANS

Answer 1

Answer:

x = y = z = 70°

Step-by-step explanation:

Opposite angles of a parallelogram are equal so

y = 70°

Since it's parallelogram so opposite sides are parallel and notice that angles x and z are corresponding angles of a pair of straight line , so x = z .

Again there is another corresponding angle that will be equal to 40° . Now sum of all angles in a triangle is 180° . so

$z + 40 + 70 = 180 \: \\ \\ \implies \: z = 180 - 110 = 70$

Answer 2

Answer:

x = 70°; y = 70°; z = 70°

Step-by-step explanation:

[Please note that the figure given is wrong and not to scale and so normal calculation and logic is applied]

In image:

• HO and EP are parallel
• HE and OP are parallel

So, ∠HEP + ∠OPE = 180° [Linear pair]

In image:

• ∠HEP = z + 40°
• ∠OPE = 70°

Substituting values accordingly:

z + 40° + 70° = 180°

=       z + 110° = 180°

=                 z = 180° - 110°

=                 z = 70°

∴ z = 70°

Now, z = x [Vertically opposite angles]

Thus,

z = x

= 70° = x

∴ x = 70°

Lastly, There are 2 ways to find y:

Method 1 (The easy way):

Opposite angles of a parallelogram are always equal and thus, y = 70°.

Method 2 (The hard way):

∠HEP + y = 180° [Linear pair]

In image and information gathered:

• ∠HEP = z + 40° = 70° + 40° = 110°

Substituting values accordingly:

z + 40° + y = 180°

=   110° + y = 180°

=             y = 180° - 110°

=             y = 70°

∴ y = 70°

Also, please refer to the attachment to see how I have named the angles.

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Hope it helps

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