Question

what is the value of v?
s
82°
r
q
v =
submit

Explanation:

Step1: Use the property of isosceles triangle

In a triangle, if two sides are equal (marked with the same tick - mark), then the angles opposite those sides are equal. So, in \(\triangle SQR\), \(\angle Q=\angle R = v\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(\angle S+\angle Q+\angle R = 180^{\circ}\). Since \(\angle S = 82^{\circ}\) and \(\angle Q=\angle R = v\), we have the equation \(82^{\circ}+v + v=180^{\circ}\).

Step3: Solve the equation for \(v\)

Combine like terms: \(82^{\circ}+2v=180^{\circ}\).
Subtract \(82^{\circ}\) from both sides: \(2v=180^{\circ}- 82^{\circ}=98^{\circ}\).
Divide both sides by 2: \(v=\frac{98^{\circ}}{2}=49^{\circ}\).

Answer:

\(49\)