Calculate Angle D: Similar Triangles with 50° Angle and Isosceles Properties

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

AAABBBCCCDDDEEE

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Step-by-step video solution

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00:00 Find angle D
00:03 The angle size according to the given data
00:06 Isosceles triangle according to the given data
00:11 In an isosceles triangle, base angles are equal, marked as A
00:16 The sum of angles in a triangle equals 180
00:23 Insert appropriate values and solve for A
00:35 This is angle A's size
00:38 The triangles are similar according to the given data
00:42 Angles are equal due to similarity
00:53 This is the solution to the question

Step-by-step written solution

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1

Understand the problem

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

AAABBBCCCDDDEEE

2

Step-by-step solution

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:

18050=130 180-50=130

130:2=65 130:2=65

As the triangles are similar, DE is parallel to BC

Angles B and D are corresponding and, therefore, are equal.

B=D=65

3

Final Answer

65 65 °

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Indicates which angle is greater

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