Answer:
54°
Step-by-step explanation:
The ratio values can be used to find the angles, then the desired difference can be found. Alternatively, the desired difference can be figured in terms of the ratio units given.
<h3>Ratio of difference to whole</h3>
The number of ratio units representing the largest angle is 5. The number of ratio units representing the smallest angle is 2. The difference of these is 5 -2 = 3.
The total number of ratio units is 3 +2 +5 = 10. This is the number of ratio units representing the straight angle, 180°.
The difference is 3 of those 10 ratio units:
3/10 × 180° = 54° . . . . . . largest - smallest difference
<h3>Find the angles</h3>
There are 10 ratio units in total (3+2+5=10), so each represents 180°/10 = 18°. Multiplying the given ratios by 18° gives the angle values:
3×18° : 2×18° : 5×18° = 54° : 36° : 90°
The difference between the largest and smallest is ...
90° -36° = 54° . . . . . . largest - smallest difference
If the side lengths of the base (12) are equal, then they are both 6. so the answer rounded to the nearest tenth is 148.7
