Question

What is the value of y? Enter your answer in the box. y = An isosceles triangle with vertices labeled A, B, and C. Side B C is the base. Sides A B and A C are equal. Sides A B and A C are labeled with single tick marks. Angle A is labeled as left parenthesis 4 y plus 10 right parenthesis degrees, angle B is labeled as 75 degrees, and angle C is labeled as left parenthesis 3 x right parenthesis degrees.

Answer 1

Answer:

$y = 5$

Step-by-step explanation:

Given:

An isosceles triangle ABC with AB = AC.

∠A = $(4y+10)\°$

∠B = $75\°$

∠C = $(3x)\°$

We know that, for an isosceles triangle, the angles opposite equal sides are also equal to each other.

Therefore, ∠B = ∠C

⇒ $75 = 3x$

⇒ $x=\frac{75}{3}=25$

∴ ∠C = $3\times 25=75$°

Now, the sum of all the interior angles of a triangle is always 180°.

$\angle A + \angle B + \angle C=180\\(4y+10)+75+75=180\\4y+10+150=180\\4y+160=180\\4y=180-160\\4y=20\\y=\frac{20}{4}=5$

Therefore, the value of 'y' is 5.