Question

geometry > n.2 triangles and bisectors gwe
what is the value of a?
diagram of triangle with right angles, segments, and angle labels 2a and a+3°
a = \boxed{\circ}
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Explanation:

Step1: Recognize Angle Bisector

Since \( EC \) is equidistant from \( ED \) and \( EF \) (perpendicular segments are equal and marked with ticks), \( E \) bisects the angle between \( ED \) and \( EF \). So \( 2a = a + 3^\circ \).

Step2: Solve for \( a \)

Subtract \( a \) from both sides: \( 2a - a = a + 3^\circ - a \), which simplifies to \( a = 3^\circ \).

Answer:

\( 3 \)