Question

solve for the value of p.
(5p+7)°
(4p+2)°

Explanation:

Answer:

To solve for \( p \), we recognize that the two angles \( (5p + 7)^\circ \) and \( (4p + 2)^\circ \) are complementary (they form a right angle, so their sum is \( 90^\circ \))? Wait, no—actually, looking at the diagram, the two angles are adjacent and form a straight line? Wait, no, the vertical line is straight, so the sum of the two angles should be \( 90^\circ \)? Wait, no, the vertical line is a straight line, but the two angles are between a vertical line and a horizontal-like line? Wait, no, the diagram shows a vertical line with two angles: \( (5p + 7)^\circ \) and \( (4p + 2)^\circ \), which together form a right angle? Wait, no, actually, the two angles are adjacent and their sum is \( 90^\circ \)? Wait, no, the vertical line is straight, so if the two angles are on one side of the vertical line, their sum should be \( 90^\circ \)? Wait, no, let's check:

Wait, the diagram has a vertical line (up and down arrows) and a line going to the right, forming two angles: \( (5p + 7)^\circ \) and \( (4p + 2)^\circ \). These two angles are adjacent and form a right angle? Wait, no, actually, they form a straight angle? Wait, no, the vertical line is straight, so the sum of the two angles should be \( 90^\circ \)? Wait, no, maybe they are complementary? Wait, no, let's think again.

Wait, the two angles are \( (5p + 7)^\circ \) and \( (4p + 2)^\circ \), and they are adjacent, forming a right angle (since the vertical line and the horizontal-like line would form a right angle). Wait, no, the vertical line and the line to the right—if the vertical line is straight, then the two angles should add up to \( 90^\circ \)? Wait, no, maybe they are supplementary? Wait, no, the vertical line is straight, so if the two angles are on one side, their sum should be \( 180^\circ \)? Wait, no, the diagram shows a vertical line with a line coming out to the right, creating two angles: one above the right line and one below. Wait, maybe the two angles are complementary (sum to \( 90^\circ \))? Wait, no, let's check the problem again.

Wait, the problem is to solve for \( p \), and the two angles are \( (5p + 7)^\circ \) and \( (4p + 2)^\circ \). Let's assume that they are complementary (sum to \( 90^\circ \)) because the diagram looks like a right angle. So:

\( (5p + 7) + (4p + 2) = 90 \)

Combine like terms:

\( 9p + 9 = 90 \)

Subtract 9 from both sides:

\( 9p = 81 \)

Divide both sides by 9:

\( p = 9 \)

Wait, but let's check again. If the two angles are adjacent and form a right angle, then their sum is \( 90^\circ \). So:

\( 5p + 7 + 4p + 2 = 90 \)

\( 9p + 9 = 90 \)

\( 9p = 81 \)

\( p = 9 \)

Yes, that makes sense. So the value of \( p \) is 9.

Wait, but maybe the two angles are supplementary? Let's check: if they are supplementary, sum to \( 180^\circ \), then:

\( 5p + 7 + 4p + 2 = 180 \)

\( 9p + 9 = 180 \)

\( 9p = 171 \)

\( p = 19 \)

But the diagram looks like a right angle, so probably complementary. Let's confirm with the diagram: the vertical line and the line to the right—if the vertical line is straight, and the line to the right is horizontal, then the two angles would be complementary (sum to \( 90^\circ \)). So the correct equation is \( (5p + 7) + (4p + 2) = 90 \), leading to \( p = 9 \).

So the answer is \( p = 9 \).