To determine which triangle matches the description given, we start by identifying the angles and the side lengths provided.
We know:
- One angle is \( 65^\circ \)
- Another angle is \( 46^\circ \)
- The side length that joins these two angles is \( 7.2 \).
First, we can find the measure of the third angle in the triangle using the fact that the sum of angles in a triangle equals \( 180^\circ \).
\[ \text{Angle C} = 180^\circ - (65^\circ + 46^\circ) = 180^\circ - 111^\circ = 69^\circ \]
Now, the key characteristics of the triangle we need to match are:
- Angles: \( A = 65^\circ \), \( B = 46^\circ \), and \( C = 69^\circ \)
- The side joining angles \( A \) and \( B \) (which is side AB) has a length of \( 7.2 \).
Next, let's evaluate the provided triangle options:
-
Option 1:
- Angles: \( 65^\circ, 46^\circ, 69^\circ \)
- Side \( AB = 7.2 \)
-
Option 2:
- Angles: \( 65^\circ, 69^\circ, 46^\circ \)
- Side \( AB = 7.2 \) (but angles do not match as expected)
-
Option 3:
- Angles: \( 46^\circ, 69^\circ, 65^\circ \)
- Side \( AB = 7.2 \) (but angles do not match as expected)
The only triangle that matches both the angle measures and the side length \( AB = 7.2 \) is Option 1.
Final Answer: Triangle ABC where angle A equals 65 degrees, angle B equals 46 degrees, angle C equals 69 degrees, side AB equals 7.2, side BC equals 7, & side AC equals 5.5.