Respuesta :
Answer:
[tex] y = 5[/tex]
Step-by-step explanation:
Given:
An isosceles triangle ABC with AB = AC.
∠A = [tex](4y+10)\°[/tex]
∠B = [tex] 75\°[/tex]
∠C = [tex](3x)\°[/tex]
We know that, for an isosceles triangle, the angles opposite equal sides are also equal to each other.
Therefore, ∠B = ∠C
⇒ [tex]75 = 3x[/tex]
⇒ [tex]x=\frac{75}{3}=25[/tex]
∴ ∠C = [tex]3\times 25=75[/tex]°
Now, the sum of all the interior angles of a triangle is always 180°.
[tex]\angle A + \angle B + \angle C=180\\(4y+10)+75+75=180\\4y+10+150=180\\4y+160=180\\4y=180-160\\4y=20\\y=\frac{20}{4}=5[/tex]
Therefore, the value of 'y' is 5.
