Question

please help me with this. fast​

Answer 1

Answer:

The measures of the angles are,

X = 40°, y = 80°, Z = 100°

Step-by-step explanation:

Refer to the attachment for solution.

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Answer 2

Answer :-

• The value of x = 40°.
• The value of y = 80°.
• The value of z = 100°.

Step-by-step explanation :-

We will find all the variables one by one by using various properties of angles and triangles.

Let's start with z.

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$\mid \underline{\fbox{ \sf To find the value of z :-}} \mid$

As we can see, z lies in the ∆ BDC.

Here,

∠ B = 30°.

∠ C = 50°.

∠ D = z.

So, we have to find ∠ D.

Here, we know the two angles of the triangle. We have to find the third one.

We know that :-

Sum of all the angles in a triangle is equal to 180°.

That means, all the three angles must be equal to 180°.

$\sf\implies z + 30^{\circ} + 50^{\circ} = 180^{\circ}$

Adding 30° and 50°,

$\sf\implies z + 80^{\circ} = 180^{\circ}$

Transposing 80° from LHS to RHS, changing its sign,

$\sf \implies z = 180^{\circ} - 80^{\circ}$

Subtracting the numbers,

$\underline{\boxed{\sf \implies z = 100.^{\circ}}}$

Hence z = 100°.

So, ∠ D in ∆ BDC = 100°.

Now let's find y.

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$\mid \underline{\fbox{\sf To find the value of y :-}} \mid$

As we can see, y lies in the ∆ BDA.

We can also see that y and z form a linear pair.

We know that :-

Linear pair = 180°.

So, y and z must be equal to 180°.

$\sf \implies y + z = 180^{\circ}$

Substituting the value of x,

$\sf \implies y + 100^{\circ} = 180^{\circ}$

Transposing y from LHS to RHS, changing it's sign,

$\sf \implies y = 180^{\circ} - 100^{\circ}$

Subtracting the numbers,

$\underline{\boxed{\sf \implies y = 80^{\circ}.}}$

Hence y = 80°.

So, ∠ D in ∆ BDA = 80°.

Now finally let's find x.

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$\mid \underline{\fbox{\sf To find the value of x :-}} \mid$

As we can see, x also lies in the ∆ BDA.

Here,

∠ B = 60°.

∠ D = 80°.

∠ A = x.

So we have to find ∠ A.

Here, we know the value of the two angles of the triangle. We have to find the third one.

We know that :-

Sum of all the angles in a triangle is equal to 180°.

That means, all the three angles must be equal to 180°.

$\sf \implies x + 60^{\circ} + 80^{\circ} = 180^{\circ}$

Adding 60° and 80°,

$\sf \implies x + 140^{\circ} = 180^{\circ}$

Transposing 140° from LHS to RHS, changing it's sign,

$\sf \implies x = 180^{\circ} - 140^{\circ}$

Subtracting the numbers,

$\underline{ \boxed{\implies \sf x = 40^{\circ}.}}$

Hence x = 40°.

So, ∠ A = 40°.

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