Triangle ADE is similar to isosceles triangle ABC.
Angle A is equal to 50°.
Calculate angle D.
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Triangle ADE is similar to isosceles triangle ABC.
Angle A is equal to 50°.
Calculate angle D.
Triangle ABC is isosceles, therefore angle B is equal to angle C. We can calculate them since the sum of the angles of a triangle is 180:
As the triangles are similar, DE is parallel to BC
Angles B and D are corresponding and, therefore, are equal.
B=D=65
°
Find the measure of the angle \( \alpha \)
Look at the position and parallel lines! Since DE is parallel to BC, angle D is in the same position as angle B. The vertices are listed in corresponding order: A↔A, D↔B, E↔C.
Isosceles triangles have two equal sides, which create two equal base angles. Since angle A = 50°, the remaining 130° is split equally: 130° ÷ 2 = 65° each.
The problem states triangle ABC is isosceles. This means two of its sides are equal, making angles B and C equal (the base angles opposite the equal sides).
No! For this problem, you only need the fact that corresponding angles are equal in similar triangles. The side ratios aren't needed to find angle measures.
Verify that all angles in triangle ADE sum to 180°: . Also check that triangle ABC angles sum correctly with the same base angles.
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