College

Given: Side AD is congruent to Side BD,

m < E = 90 degrees, and m < DBA = 24 degrees. Solve for m < EAD

1. 24 degrees

2. 42 degrees

3. 48 degrees

4. 66 degrees

Given Side AD is congruent to Side BD m E 90 degrees and m DBA 24 degrees Solve for m EAD 1 24 degrees 2

Answer :

The problem involves triangles ADE and BDC. Given angle E = 90° and angle DBA = 24°. By triangle properties, angle EAD is solved as 45°.

Since triangle ADE and triangle BDC share side AD, we can use the property that the sum of angles in a triangle is 180 degrees.

Given:

- Angle E is 90 degrees.

- Angle DBA is 24 degrees.

In triangle BDC, angle BDC = 180 - 90 - 24 = 66 degrees.

Since AD is congruent to BD, triangle ADE is an isosceles triangle. Therefore, angle EAD = angle EDA.

In triangle ADE, angle EAD + angle EDA + angle A = 180 degrees.

Since angle EAD = angle EDA, let's denote both as x.

So, x + x + 90 = 180.

2x + 90 = 180.

2x = 180 - 90.

2x = 90.

x = 45.

Therefore, angle EAD = 45 degrees.

So, the correct answer is option 1. 45 degrees.

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