Triangle ADE is similar to isosceles triangle ABC.
Angle A is equal to 50°.
Calculate angle D.
We have hundreds of course questions with personalized recommendations + Account 100% premium
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
°
a is parallel to b.
Calculate the angles shown in the diagram.
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.
Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime