Respuesta :
Part a: The value of x is 33°
Part b: The measure of each base angle is 69°
Explanation:
It is given that the vertex angle of an isosceles triangle measures 42°.
The base angle in the triangle has a measure of [tex](2x+3)^{\circ}[/tex]
Part a: To determine the value of x
Since, in an isosceles triangle the base angles are always equal.
Thus, the three angles in an isosceles triangle add up to 180°
Hence, we have,
[tex]42+2x+3+2x+3=180[/tex]
[tex]42+4x+6=180[/tex]
[tex]4x+48=180[/tex]
[tex]4x=132[/tex]
[tex]x=33^{\circ}[/tex]
Thus, the value of x is 33°
Part b: To find the measure of each base angle.
Base angle = [tex](2 x+3)^{\circ}[/tex]
Substituting [tex]x=33^{\circ}[/tex] , we get,
[tex]Base \ angle = (2(33)+3)^{\circ}[/tex]
[tex]=(66+3)^{\circ}[/tex]
[tex]=69^{\circ}[/tex]
Thus, the measure of each base angle is 69°
Answer:
33 and 69 lol funny number
Step-by-step explanation:
