Question

in the diagram below, ( ab parallel cd ), ( ef parallel gh ), and ( mangle ikl = 63^{circ} ). find ( mangle ajg ).
step
angle
reason
1
( mangle ikl = 63^{circ} )
given
try ( manglesquare=square^{circ} )
select a reason
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Explanation:

Step1: Find the measure of \(\angle ILK\)

Since \(\angle IKL = 63^{\circ}\) and \(\angle ILK\) and \(\angle IKL\) are vertical angles. Vertical angles are equal.
\(m\angle ILK=m\angle IKL = 63^{\circ}\)

Step2: Find the measure of \(\angle AJG\)

Because \(EF\parallel GH\) and \(AB\) is a transversal. When two parallel lines are cut by a transversal, corresponding angles are equal. \(\angle AJG\) and \(\angle ILK\) are corresponding angles.
\(m\angle AJG=m\angle ILK = 63^{\circ}\)

Answer:

\(m\angle AJG = 63^{\circ}\)