Answer:
Each base angle would be 70°.
Step-by-step explanation:
<em>*</em><em>Base angles means the two equal angles formed on the base are called base angles.</em>
<em> </em><em>B</em><em>ase means the third unequal side of the triangle.</em><em> </em><em>*</em>
Given triangle is isosceles triangle.
The angle of vertex which is given is <u>40°</u>.
Let each base angle be <em>x</em>.
We know that,
<em>There are two base angles in a isosceles triangle</em>.
And, Sum of angles of triangle is 180° .
Therefore,
![\tt \implies \: x + x + 40 {}^{ \circ} = 180 {}^\circ](https://tex.z-dn.net/?f=%20%5Ctt%20%5Cimplies%20%5C%3A%20x%20%2B%20x%20%20%20%2B%2040%20%7B%7D%5E%7B%20%5Ccirc%7D%20%20%3D%20180%20%7B%7D%5E%5Ccirc)
Now Solve For <em>x</em>. That would be the solution.
Steps:
<u>Combine like terms:</u>
![\tt \implies2x + 40{}^{ \circ} = 180{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies2x%20%2B%2040%7B%7D%5E%7B%20%5Ccirc%7D%20%20%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20)
<u>Subtract 40 from both sides:</u>
![\tt \implies2x + 40{}^{ \circ} - 40 = 180{}^{ \circ} - 40{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies2x%20%2B%2040%7B%7D%5E%7B%20%5Ccirc%7D%20%20-%2040%20%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20%20%20-%2040%7B%7D%5E%7B%20%5Ccirc%7D%20)
<u>Simplify </u><u>the</u><u> </u><u>LHS </u><u>and </u><u>RHS</u><u>:</u>
![\tt \implies2x + 0 = 140{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies2x%20%2B%200%20%3D%20140%7B%7D%5E%7B%20%5Ccirc%7D%20)
![\tt \implies2x = 140 {}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies2x%20%3D%20140%20%7B%7D%5E%7B%20%5Ccirc%7D%20)
<u>Divide both sides by 2:</u>
![\tt \implies \cfrac{2x}{2} = \cfrac{140{}^{ \circ} }{2{}^{ \circ} }](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%20%5Ccfrac%7B2x%7D%7B2%7D%20%20%3D%20%20%5Ccfrac%7B140%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%7B2%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%20)
<u>Use cancellation method and cancel LHS and RHS:</u>
![\tt \implies \cfrac{ \cancel2x}{ \cancel2} = \cfrac{ \cancel{140^{ \circ}} }{ \cancel{2{}^{ \circ} }}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%20%20%5Ccfrac%7B%20%5Ccancel2x%7D%7B%20%5Ccancel2%7D%20%20%3D%20%20%5Ccfrac%7B%20%5Ccancel%7B140%5E%7B%20%5Ccirc%7D%7D%20%7D%7B%20%5Ccancel%7B2%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%7D%20)
![\tt \implies \cfrac{1x}{1} = \cfrac{70{}^{ \circ} }{1{}^{ \circ} }](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%20%5Ccfrac%7B1x%7D%7B1%7D%20%20%3D%20%20%5Ccfrac%7B70%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%7B1%7B%7D%5E%7B%20%5Ccirc%7D%20%7D%20)
![\tt \implies{1x} = {70}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%7B1x%7D%20%20%3D%20%7B70%7D%5E%7B%20%5Ccirc%7D%20)
![\tt \implies{x} = 70{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%7Bx%7D%20%3D%2070%7B%7D%5E%7B%20%5Ccirc%7D%20)
Hence, each base angle would be 70°.
<u>Verification</u>:
As we know that sum of angles of triangle is 180°.
So,
![\tt \implies \: Base \: angle + other \: base \: angle + vertex \: angle= 180{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies%20%5C%3A%20Base%20%5C%3A%20%20angle%20%2B%20other%20%5C%3A%20%20base%20%5C%3A%20%20angle%20%20%2B%20vertex%20%5C%3A%20angle%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20)
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}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies70%7B%7D%5E%7B%20%5Ccirc%7D%20%20%2B%2070%7B%7D%5E%7B%20%5Ccirc%7D%20%20%2B%2040%7B%7D%5E%7B%20%5Ccirc%7D%20%20%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20)
<u>Solve it.</u>
![\tt \implies140{}^{ \circ} + 40{}^{ \circ} = 180{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies140%7B%7D%5E%7B%20%5Ccirc%7D%20%20%2B%2040%7B%7D%5E%7B%20%5Ccirc%7D%20%20%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20)
![\tt \implies180{}^{ \circ} = 180{}^{ \circ}](https://tex.z-dn.net/?f=%5Ctt%20%5Cimplies180%7B%7D%5E%7B%20%5Ccirc%7D%20%20%20%3D%20180%7B%7D%5E%7B%20%5Ccirc%7D%20)
![\tt \: LHS = RHS](https://tex.z-dn.net/?f=%20%5Ctt%20%5C%3A%20LHS%20%20%3D%20RHS)
![\star \sf \: Hence, Verified.](https://tex.z-dn.net/?f=%20%5Cstar%20%5Csf%20%5C%3A%20Hence%2C%20Verified.)
![\rule{225pt}{2pt}](https://tex.z-dn.net/?f=%20%5Crule%7B225pt%7D%7B2pt%7D)
I hope this helps!
Let me know if you have any questions.