Question

quiz pt 2 - similar triangles
120° 17°
53°
34° 129°
17°
34°
34°
63°
☑ none of the above

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). For the first triangle (top - left) with angles \(129^\circ\) and \(17^\circ\), the third angle is \(180-(129 + 17)=34^\circ\).

Step2: Check other triangles

• Top - right: Angles \(53^\circ\) (and others, but \(53

eq129,17,34\)) – not similar.

• Middle - left: Angles \(34^\circ\) and \(129^\circ\), third angle \(180-(34 + 129)=17^\circ\) – same angles as first triangle (\(129^\circ,17^\circ,34^\circ\)) so similar.
• Middle - right: Angles \(17^\circ\) and \(34^\circ\), third angle \(180-(17 + 34)=129^\circ\) – same angles as first triangle, so similar.
• Bottom - left: Angles \(34^\circ\) and \(63^\circ\), third angle \(180-(34 + 63)=83^\circ\) – different angles.

Wait, maybe the question is about which triangle is similar to the first. The first triangle has angles \(129^\circ\), \(17^\circ\), \(34^\circ\). The middle - left (angles \(34^\circ\), \(129^\circ\), \(17^\circ\)) and middle - right (angles \(17^\circ\), \(34^\circ\), \(129^\circ\)) have the same angle measures (order may differ, but similarity depends on angle equality). If the original first triangle is \(129^\circ\), \(17^\circ\), \(34^\circ\), then the middle - left (with \(34^\circ\), \(129^\circ\)) and middle - right (with \(17^\circ\), \(34^\circ\)) are similar. But the "None of the above" is checked, which is incorrect. Wait, maybe miscalculation? Wait first triangle: \(129 + 17=146\), \(180 - 146 = 34\). Middle - left: \(34+129 = 163\), \(180 - 163=17\). So angles \(34^\circ\), \(129^\circ\), \(17^\circ\) – same as first. Middle - right: \(17 + 34=51\), \(180 - 51 = 129\) – angles \(17^\circ\), \(34^\circ\), \(129^\circ\) – same. So the triangles with angles \(34^\circ\), \(129^\circ\), \(17^\circ\) (middle - left and middle - right) are similar to the first. If the "None of the above" is selected, that's wrong. But based on angle sum, the middle - left (the triangle with \(34^\circ\) and \(129^\circ\)) and middle - right (with \(17^\circ\) and \(34^\circ\)) are similar.

Answer:

The triangle with angles \(34^\circ\) and \(129^\circ\) (middle - left) and the triangle with angles \(17^\circ\) and \(34^\circ\) (middle - right) are similar to the first triangle. If we consider the options (assuming checkboxes), the middle - left (with \(34^\circ\) and \(129^\circ\)) and middle - right (with \(17^\circ\) and \(34^\circ\)) should be selected, not "None of the above". But based on the calculation, the triangles with angles \(129^\circ\), \(17^\circ\), \(34^\circ\) (in any order) are similar. So the correct triangles are the middle - left (angles \(34^\circ\), \(129^\circ\)) and middle - right (angles \(17^\circ\), \(34^\circ\)).