Question

find $m\angle egf$ and $m\angle dge$.
$m\angle egf = $
number:
$m\angle dge = $
color:

Explanation:

Step1: Set angles equal (alternate interior)

Since \(DE \parallel GF\) (opposite sides of rectangle are parallel), \(\angle DEG = \angle EGF\).
So \(11x - 10 = 2x + 17\)

Step2: Solve for \(x\)

Subtract \(2x\) and add 10 to both sides:
\(11x - 2x = 17 + 10\)
\(9x = 27\)
\(x = \frac{27}{9} = 3\)

Step3: Calculate \(m\angle EGF\)

Substitute \(x=3\) into \(2x+17\):
\(m\angle EGF = 2(3) + 17 = 6 + 17 = 23\)

Step4: Calculate \(m\angle DGE\)

\(\angle DGE\) and \(\angle EGF\) form a right angle (corner of rectangle), so:
\(m\angle DGE = 90^\circ - m\angle EGF = 90 - 23 = 67\)

Answer:

\(m\angle EGF = 23^\circ\)
\(m\angle DGE = 67^\circ\)