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

Question

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

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

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:

$180-50=130$

$130:2=65$

As the triangles are similar, DE is parallel to BC

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

B=D=65

$65$ °