Questions: Determine the value of y in the figure, and identify whether the triangle is isosceles or equilateral. y=30°; equilateral y=60°; isosceles y=30°; isosceles y=60°; equilateral

Determine the value of y in the figure, and identify whether the triangle is isosceles or equilateral.
y=30°; equilateral
y=60°; isosceles
y=30°; isosceles
y=60°; equilateral

Transcript text: Determine the value of $y$ in the figure, and identify whether the triangle is isosceles or equilateral. $y=30^{\circ}$; equilateral $y=60^{\circ}$; isosceles $y=30^{\circ}$; isosceles $y=60^{\circ}$; equilateral

Solution

Solution Steps

Step 1: Identify the sum of angles in a triangle

The sum of the interior angles in any triangle is always 180 degrees.

Step 2: Set up the equation

Given two angles are 60 degrees each, we can set up the equation to find the third angle $ y $: \[ 60^\circ + 60^\circ + y = 180^\circ \]

Step 3: Solve for $ y $

\[ 120^\circ + y = 180^\circ \] \[ y = 180^\circ - 120^\circ \] \[ y = 60^\circ \]

Step 4: Determine the type of triangle

Since all three angles are 60 degrees, the triangle is equilateral.

Final Answer

\[ y = 60^\circ \]; equilateral

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