Question

2 a triangle is shown
based on the triangle, which statements are true?
select two correct answers.
$y = 55^{\circ}$ because $60^{\circ} + 65^{\circ} = 125^{\circ}$ and $180^{\circ} - 125^{\circ} = 55^{\circ}$
$y = 125^{\circ}$ because $180^{\circ} - (60^{\circ} + 65^{\circ}) = 55^{\circ}$ and $180^{\circ} - 55^{\circ} = 125^{\circ}$
$y = 305^{\circ}$, because $60^{\circ} + 65^{\circ} = 125^{\circ}$ and $125^{\circ} + 180^{\circ} = 305^{\circ}$
$y = 175^{\circ}$ because $180^{\circ} - 65^{\circ} = 115^{\circ}$ and $115^{\circ} + 60^{\circ} = 175^{\circ}$
$x = 125^{\circ}$ because $180^{\circ} - (60^{\circ} + 65^{\circ}) = 55^{\circ}$ and $180^{\circ} - 55^{\circ} = 125^{\circ}$
$x = 55^{\circ}$ because $60^{\circ} + 65^{\circ} = 125^{\circ}$ and $180^{\circ} - 125^{\circ} = 55^{\circ}$

Explanation:

1. For angle \( x \): The sum of interior angles of a triangle is \( 180^\circ \). So, \( x = 180^\circ-(60^\circ + 65^\circ)=55^\circ \) (since \( 60 + 65 = 125 \), \( 180 - 125 = 55 \)). Also, \( x \) and \( y \) are supplementary (sum to \( 180^\circ \)), so \( y = 180^\circ - x = 125^\circ \).
2. Check each statement:

• " \( y = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)": Wrong, \( y \) is supplementary to \( x \), \( x = 55^\circ \), so \( y = 125^\circ \).
• " \( y = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)": Correct, as \( x = 55^\circ \), \( y = 180 - 55 = 125 \).
• " \( y = 305^\circ \), because \( 60^\circ+65^\circ = 125^\circ \) and \( 125^\circ+180^\circ = 305^\circ \)": Wrong, angles on a straight line sum to \( 180^\circ \), not more.
• " \( y = 175^\circ \) because \( 180^\circ - 65^\circ = 115^\circ \) and \( 115^\circ+60^\circ = 175^\circ \)": Wrong, incorrect reasoning.
• " \( x = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)": Wrong, \( x \) is an interior angle, should be \( 55^\circ \).
• " \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)": Correct, using triangle angle sum.
• The first highlighted statement " \( y = 55^\circ \)..." is wrong, the second highlighted " \( y = 125^\circ \)..." is correct. Also, " \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)" is correct. Wait, re - evaluating:
• The two correct statements are:
• " \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)" (correct, triangle angle sum).
• " \( y = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)" (correct, supplementary angles). Also, the statement " \( y = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)" and " \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)" are the two correct ones. Also, another way: The first correct statement about \( x \): \( x = 55^\circ \) (triangle angle sum: \( 180-(60 + 65)=55 \)). The second correct statement about \( y \): \( y = 125^\circ \) (since \( x + y=180 \), so \( y = 180 - 55 = 125 \)). So the two correct answers are:
• \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)
• \( y = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)

Answer:

• \( x = 55^\circ \) because \( 60^\circ+65^\circ = 125^\circ \) and \( 180^\circ - 125^\circ = 55^\circ \)
• \( y = 125^\circ \) because \( 180^\circ-(60^\circ + 65^\circ)=55^\circ \) and \( 180^\circ - 55^\circ = 125^\circ \)