Question

find the values of (x) and (y) in the following diagram:

• (x = 12) and (y = 9)
• (x = 9) and (y = 12)
• (x = 5) and (y = 14)
• (x = 14) and (y = 5)

Explanation:

Find the value of x

The angle \((2x + 10)^\circ\) and the adjacent angle \(152^\circ\) form a linear pair along a straight line.

$$ (2x + 10) + 152 = 180 $$

$$ 2x + 162 = 180 $$

$$ 2x = 18 $$

$$ x = 9 $$

Find the value of y

Using the Triangle Angle Sum Theorem, the sum of the interior angles of the right triangle must equal \(180^\circ\). The interior angles are \(90^\circ\), \((4y + 14)^\circ\), and \((2x + 10)^\circ\).
Substitute \(x = 9\) into the expression for the third angle:

$$ 2(9) + 10 = 28^\circ $$

Now, set up the sum of the angles:

$$ 90 + (4y + 14) + 28 = 180 $$

$$ 4y + 132 = 180 $$

$$ 4y = 48 $$

$$ y = 12 $$

Answer:

• \(x = 12\) and \(y = 9\)
• \(x = 9\) and \(y = 12\) (Correct answer)
• \(x = 5\) and \(y = 14\)
• \(x = 14\) and \(y = 5\)