Question

I need help its my homework and it's due today
Find the base angles.​

Answer 1

The measurements of Angle ABC = Angle ABC = 70°.

Explanation:

Understanding concept:

Here, we are given with a triangle that has two sides equal. The triangle which has two sides as equal is said to be an isosceles triangle. The triangle which has two sides equal will also have two angles equal and the other different. In this question, we are given with the measurement of an angle of isosceles triangle. We are asked to find the other angle in this triangle. To find. the answer, we use the concept of angle sum property of the triangle. Thai concept says that all the angles in a triangle together adds up to 180°. If no, then it's not considered as a triangle.

Solution:

Angles sum property of a triangle (∆) = 180°

Angle BAC + Angle ABC + Angle ACB = 180°

Substitute all the given values then

→ 40° + x° + x° = 180°

Add the variables together .i.e., x° + x° is 2x.

→ 40° + 2x° = 180°

Shift, the number 40° from LHS to RHS, changing it's sign.

→ 2x° = 180° - 40°

Subtract the values on RHS.

→ 2x° = 140°

Shift the number 2° from LHS to RHS.

→ x° = 140°/2°

Simplify the fraction to get the value of x.

→ x° = 70°

Therefore, x = 70°

Answer: Hence, the measurement of both the base unknown angles x is 70°.

Explore More:

Let's check whether the values of x is true or false.

Verification:

If the values of x = 70° then the equation is

40° + x° + x° = 180°

Substitute the values of x = 70° then

→ 40° + 70° + 70° = 180°

Add the values on LHS.

→ 40° + 140° = 180°

→ 180° = 180°

LHS = RHS is true for x = 70°

Hence, verified.

Please let me know if you have any other questions.

Answer 2

Each base angle would be 70°.

Explanation:

*Base angles means the two equal angles formed on the base are called base angles.

Base means the third unequal side of the triangle. *

Given triangle is isosceles triangle.

The angle of vertex which is given is 40°.

Let each base angle be x.

We know that,

There are two base angles in a isosceles triangle.

And, Sum of angles of triangle is 180° .

Therefore,

`\tt \implies \: x + x + 40 {}^( \circ) = 180 {}^\circ`

Now Solve For x. That would be the solution.

Steps:

Combine like terms:

`\tt \implies2x + 40{}^( \circ) = 180{}^( \circ)`

Subtract 40 from both sides:

`\tt \implies2x + 40{}^( \circ) - 40 = 180{}^( \circ) - 40{}^( \circ)`

Simplify the LHS and RHS:

`\tt \implies2x + 0 = 140{}^( \circ)`

`\tt \implies2x = 140 {}^( \circ)`

Divide both sides by 2:

`\tt \implies \cfrac{2x}{2} = \cfrac{140{}^( \circ) }{2{}^( \circ) }`

Use cancellation method and cancel LHS and RHS:

`\tt \implies \cfrac{ \cancel2x}{ \cancel2} = \cfrac{ \cancel{140^( \circ)} }{ \cancel{2{}^( \circ) }}`

`\tt \implies \cfrac{1x}{1} = \cfrac{70{}^( \circ) }{1{}^( \circ) }`

`\tt \implies{1x} = {70}^( \circ)`

`\tt \implies{x} = 70{}^( \circ)`

Hence, each base angle would be 70°.

Verification:

As we know that sum of angles of triangle is 180°.

So,

`\tt \implies \: Base \: angle + other \: base \: angle + vertex \: angle= 180{}^( \circ)`

We got that one base angles of the given isosceles triangle is 70° and other is 70°, and the vertex angle is 40°[Given].

`\tt \implies70{}^( \circ) + 70{}^( \circ) + 40{}^( \circ) = 180{}^( \circ)`

Solve it.

`\tt \implies140{}^( \circ) + 40{}^( \circ) = 180{}^( \circ)`

`\tt \implies180{}^( \circ) = 180{}^( \circ)`

`\tt \: LHS = RHS`

`\star \sf \: Hence, Verified.`

`\rule{225pt}{2pt}`

I hope this helps!

Let me know if you have any questions.