Question

neko made a triangular flag shown below. he wanted to attach it to the stick and then trim off the extra fabric so the flag would form an isosceles triangle. by how many degrees was he off when he attached the triangle to the stick?

a. his flag ended up with base angles of ( 86^{circ} ) and ( 62^{circ} ), so the stick was ( 12^{circ} ) out of alignment from the correct position (both angles ( 74^{circ} )).
b. his flag ended up with base angles of ( 86^{circ} ) and ( 52^{circ} ), so the stick was ( 22^{circ} ) out of alignment from the correct position (both angles ( 74^{circ} )).
c. his flag ended up with base angles of ( 28^{circ} ) and ( 62^{circ} ), so the stick was ( 34^{circ} ) out of alignment from the correct position (both angles ( 62^{circ} )).
d. his flag ended up with base angles of ( 28^{circ} ) and ( 62^{circ} ), so the stick was ( 34^{circ} ) out of alignment from the correct position (both angles ( 34^{circ} )).

Explanation:

Step1: Encontrar el tercer ángulo del triángulo

La suma de los ángulos adyacentes a un lado es \(180^{\circ}\). Si un ángulo es \(118^{\circ}\), entonces el ángulo interior del triángulo es \(180 - 118=62^{\circ}\).

Step2: Calcular el tercer ángulo del triángulo original

La suma de los ángulos de un triángulo es \(180^{\circ}\). Dados dos ángulos \(32^{\circ}\) y \(62^{\circ}\), el tercer ángulo es \(180-(32 + 62)=86^{\circ}\).

Step3: Encontrar el ángulo correcto para un triángulo isósceles

Si el triángulo es isósceles, los ángulos base son iguales. La suma de los ángulos de un triángulo es \(180^{\circ}\). Entonces, cada ángulo base es \(\frac{180 - 32}{2}=74^{\circ}\).

Step4: Calcular la diferencia

La diferencia entre \(86^{\circ}\) y \(74^{\circ}\) es \(86 - 74 = 12^{\circ}\), y la diferencia entre \(62^{\circ}\) y \(74^{\circ}\) es \(74 - 62=12^{\circ}\).

Answer:

A. His flag ended up with base angles of \(86^{\circ}\) and \(62^{\circ}\), so the stick was \(12^{\circ}\) out of alignment from the correct position (both angles \(74^{\circ}\)).