Question

solve for the value of q.
(4q-5)°
(5q+5)°
answer attempt 1 out of 2
q =
submit answer

Explanation:

Step1: Identify angle sum

The angles around a point on a straight line (or here, the sum of these angles with the right angle) should be \(180^\circ\) (since they form a linear pair with the right angle? Wait, actually, looking at the diagram, there's a right angle (\(90^\circ\)), and the two angles \((4q - 5)^\circ\) and \((5q + 5)^\circ\) along with the right angle should add up to \(180^\circ\)? Wait, no, actually, the three angles: the right angle (\(90^\circ\)), \((4q - 5)^\circ\), and \((5q + 5)^\circ\) are adjacent and form a straight line (since they are on a straight line), so their sum is \(180^\circ\). Wait, no, the right angle is between the vertical and horizontal, and the other two angles are on either side. Wait, actually, the sum of \((4q - 5)^\circ\), \(90^\circ\), and \((5q + 5)^\circ\) should be \(180^\circ\)? Wait, no, that can't be. Wait, looking at the diagram, the two angles \((4q - 5)^\circ\) and \((5q + 5)^\circ\) and the right angle: actually, the straight line is \(180^\circ\), so \((4q - 5) + 90 + (5q + 5) = 180\)? Wait, no, let's check: \((4q - 5) + (5q + 5) + 90 = 180\)? Wait, no, that would be \(9q + 90 = 180\), so \(9q = 90\), \(q = 10\). Wait, let's do it step by step.

Step1: Set up the equation

The sum of the angles on a straight line is \(180^\circ\). Here, we have a right angle (\(90^\circ\)), angle \((4q - 5)^\circ\), and angle \((5q + 5)^\circ\). So:

$$ (4q - 5) + 90 + (5q + 5) = 180 $$

Step2: Simplify the left side

Combine like terms:
\(4q - 5 + 90 + 5q + 5 = (4q + 5q) + (-5 + 5 + 90) = 9q + 90\)

Step3: Solve for \(q\)

Set equal to \(180\):

$$ 9q + 90 = 180 $$

Subtract \(90\) from both sides:

$$ 9q = 180 - 90 = 90 $$

Divide both sides by \(9\):

$$ q = \frac{90}{9} = 10 $$

Answer:

\(q = 10\)