The problem from the image states:

"The larger of two supplementary angles exceeds 7 times the smaller by 4°. Find the measure of the larger angle."

Let's break this down:

Let:

• $x$ be the smaller angle.
• $y$ be the larger angle.

Step 1: Relationship between supplementary angles

Supplementary angles add up to 180°: $x + y = 180$

Step 2: The given condition

The larger angle exceeds 7 times the smaller angle by 4°: $y = 7x + 4$

Step 3: Substitution

Substitute $y = 7x + 4$ into $x + y = 180$: $x + (7x + 4) = 180$ $x + 7x + 4 = 180$ $8x + 4 = 180$

Step 4: Solve for $x$

$8x = 180 - 4$ $8x = 176$ $x = \frac{176}{8} = 22$

Step 5: Find $y$

Now that $x = 22$, substitute it back into $y = 7x + 4$: $y = 7(22) + 4 = 154 + 4 = 158$

Final Answer:

The larger angle is $158^\circ$.

Would you like more details or have any further questions?

Here are 5 related questions to extend your understanding:

1. What would the value of the larger angle be if it exceeded 6 times the smaller angle by 5°?
2. How would the solution change if the angles were complementary instead of supplementary?
3. If the larger angle were twice the smaller angle, how would you solve it?
4. What are the angles if the difference between the larger and smaller angle is 60°?
5. Can two supplementary angles both be acute?

Tip: Always check the conditions given in angle problems carefully, such as supplementary, complementary, or other relationships!