Question

In triangle DEF, if angle E is three times angle D and angle F is 9° less than angle E, what is the measure of each angle? Angle D = _____°, Angle E = _____°, Angle F = _____°

Answer 1

To solve for the angles in triangle DEF, set up equations based on the given relationships and the fact that the sum of angles in a triangle is 180°. Through this process, we find that Angle D is 27°, Angle E is 81°, and Angle F is 72°.

Step-by-step explanation:

In triangle DEF, we have two conditions: angle E is three times angle D and angle F is 9° less than angle E. Because the sum of angles in any triangle is always 180°, we can set up the following equations to find the measures of the angles:

1. Let angle D = x degrees.
2. Then angle E = 3x degrees (since it is three times angle D).
3. And angle F = 3x − 9° (since it is 9° less than angle E).
4. The sum of the angles is x + 3x + (3x − 9°) = 180°.
5. This simplifies to 7x − 9° = 180°.
6. Solving for x gives us x = (180° + 9°) / 7, which is x = 27°.
7. So, angle D = 27°, angle E = 3 * 27° = 81°, and angle F = 81° − 9° = 72°.

Therefore, the measures of the angles are: Angle D = 27°, Angle E = 81°, and Angle F = 72°.