https://file.aiquickdraw.com/mathbot/file/1726842912686w42resii.jpg

The image shows two angles that form a right angle together. The sum of these two angles should be equal to 90°.

Given:
- The first angle is \((8y + 7)^\circ\).
- The second angle is \((7y + 8)^\circ\).

We can set up the equation:

\[
(8y + 7) + (7y + 8) = 90
\]

Let's solve this equation for \( y \).The value of \( y \) is \( 5 \).

Now let's find the actual measures of both angles:

1. \((8y + 7)^\circ\)
2. \((7y + 8)^\circ\)

Substitute \( y = 5 \) into each expression to get their values.The angles are:

1. \( (8y + 7)^\circ = 47^\circ \)
2. \( (7y + 8)^\circ = 43^\circ \)

These two angles add up to 90°, confirming that they form a right angle.

Would you like more details or have any questions?

Here are some related questions:

1. What happens to the angle values if \( y \) is doubled?
2. How would the angle expressions change if they summed up to a different value, such as 180°?
3. What is the geometric significance of these angles in a coordinate plane?
4. How do complementary and supplementary angles differ in properties?
5. Can you find other pairs of values for different variables that would still satisfy the right angle condition?

**Tip:** When solving linear equations with a single variable, always isolate the variable on one side to find the solution efficiently.

Solve for y in the given angle relationship: The sum of two angles is 90°, where the first angle is (8y + 7)° and the second angle is (7y + 8)°.

In this problem, we solve for y where two algebraic expressions represent complementary angles that add up to 90°. Explore step-by-step how to solve the linear equation and find the actual angle measures. Suitable for students in Grades 7-9.

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