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Sagot :
Given:
An isosceles triangle has an angle that measures 40°.
To find:
The other possible angles of the triangle.
Solution:
Case 1: 40° is the measure of base angle of isosceles triangle.
Then, the other base angle is 40°.
Let x be the measure of third angle.
The sum of all interior angles of a triangle is 180 degrees. So,
[tex]x+40^\circ+40^\circ=180^\circ[/tex]
[tex]x=180^\circ-40^\circ-40^\circ[/tex]
[tex]x=100^\circ[/tex]
So, the possible angles are 40° and 100°.
Case 2: 40° is the measure of vertical angle of isosceles triangle.
Let y be the measure of base angles, then
[tex]y+y+40^\circ=180^\circ[/tex]
[tex]2y=180^\circ -40^\circ[/tex]
[tex]y=\dfrac{140^\circ}{2}[/tex]
[tex]y=70^\circ [/tex]
So, the possible angles are 40° and 70°.
Therefore, the correct options are A, B and D.
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