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olga nikolaevna [1]
3 years ago
15

If 3y+5=7x, then 21y-49x=?

Mathematics
1 answer:
FromTheMoon [43]3 years ago
3 0
3y+5=7x

3y=7x-5

y=(7x-5)/3

...

21y-49x becomes

7(7x-5)-49x

49x-35-49x

-35
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We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use
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Question has missing figure, the figure is in the attachment.

Answer:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

Step-by-step explanation:

Given,

We have an isosceles triangle which we can named it as ΔABC.

In which Length of AB is equal to length of BC.

And also m∠B is equal to m∠C.

ext.m∠C= 115°(Here ext. stands for exterior)

We have to find the measure of angles angles 1 through 5.

Solution,

For ∠1.

∠1 and ext.∠C makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle1+ext.\angle C=180\°

On putting the values, we get;

\angle 1+115\°=180\°\\\\\angle1=180\[tex]\therefore m\angle2=65\°-115\°=65\°[/tex]

Thus the measure of ∠1 is 65°.

For ∠2.

Since the given triangle is an isosceles triangle.

So, m\angle1=m\angle2

Thus the measure of ∠2 is 65°.

For ∠3.

Here ∠1, ∠2 and ∠3 are the three angles of the triangle.

So we use the angle sum property of triangle, which states that;

"The sum of all the angles of a triangle is equal to 180°".

\therefore \angle1+\angle2+\angle3=180\°

Now we put the values and get;

65\°+65\°+\angle3=180\°\\\\130\°+\angle3=180\°\\\\\angle3=180\°-130\°=50\°

Thus the measure of ∠3 is 50°.

For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle2 +\angle 4 =180\°

Substituting the values of of angle 2 to find angle 4 we get;

65\°+ \angle 4 = 180\°\\\\ \angle 4 = 180\°-65\°\\\\\angle 4= 115\°

Thus the measure of ∠4 is 115°.

For ∠5.

∠4 and ∠5 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

\angle4 +\angle 5 =180\°

Substituting the values of of angle 4 to find angle 5 we get;

115\°+ \angle 5 = 180\°\\\\ \angle 5 = 180\°-115\°\\\\\angle 5= 65\°

Thus the measure of ∠5 is 65°.

Hence:

The measure of ∠1 is 65°.

The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

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