Question

We have seen that isosceles triangles have two sides of equal length. The angles opposite these sides have the same measure. Use the information to the right to help find the measure of angles 1 through 5.

Answer 1

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°.

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°.