In this diagram, we have intersecting lines that form several angles. We are given two angles: $70^\circ$ and $87^\circ$. These angles are used to find the missing angles $d$, $e$, and $f$.

Step-by-step Explanation:

1. Angle $d$: Angle $d$ is a vertical angle to the $87^\circ$ angle. Vertical angles are always equal, so: $d = 87^\circ$

2. Angle $e$: Angle $e$ is a vertical angle to the $70^\circ$ angle. Vertical angles are also equal, so: $e = 70^\circ$

3. Angle $f$: Angle $f$ forms a linear pair with the $70^\circ$ angle. Since angles on a straight line add up to $180^\circ$, we can find $f$ as: $f = 180^\circ - 70^\circ = 110^\circ$

Final Answer:

• $d = 87^\circ$
• $e = 70^\circ$
• $f = 110^\circ$

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Related Questions:

1. How do we calculate angles in polygons?
2. What is the sum of angles in a triangle, and how can it help solve problems like this?
3. Can you explain the difference between vertical angles and adjacent angles?
4. How do we apply the concept of supplementary angles in more complex figures?
5. What are corresponding angles and how do they relate to parallel lines?

Tip:

Always remember that vertical angles are equal, and adjacent angles formed by a straight line sum to $180^\circ$.