Question

BGE is a triangle such that BG = GE. Show that the angle marked x is 80°.

ignore my markings they r prolly wrong

Answer 1

The angle marked x is 80°. angle BGE and angle EGB are congruent. Considering the sum of angles in a triangle is 180°, and given that angle BGE = angle EGB = x, the total of these two angles is 2x. As BG = GE, angle BGE = angle EGB = x = 40°.

Explanation:

In triangle BGE where BG = GE, the angles opposite equal sides are also equal. Therefore, angle BGE and angle EGB are congruent. Considering the sum of angles in a triangle is 180°, and given that angle BGE = angle EGB = x, the total of these two angles is 2x. As BG = GE, angle BGE = angle EGB = x = 40°.

Hence, angle x, marked in the diagram, is 80° (2x = 2 * 40° = 80°). This is derived from the fact that the angles around point G add up to 180°, and in this case, the three angles are x, x, and 60° (as they form a straight line), leading to x = 40°, making the marked angle x equal to 80°.

The angle marked x is 80°. angle BGE and angle EGB are congruent. Considering the sum of angles in a triangle is 180°, and given that angle BGE = angle EGB = x, the total of these two angles is 2x. As BG = GE, angle BGE = angle EGB = x = 40°.