Question

The angle opposite to the equal angle of an isosceles triangle measures 30°. Find the measure of the other two angles of the triangles.​

Answer 1

Answer:

75°

Step-by-step explanation:

Sum of all the angles of the triangle= 180°

Let the two angles be x

30+x+x=180

2x= 180-30= 150

x=150/2

x= 75°

Hope it helps

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Answer 2

Step-by-step explanation:

Let G1,G2 denote the centroids of triangles ABD and ACD.

Then G1,G2 lie on the line parallel to BC that passes through the centriod of triangle ABC.

∴BG1G2C is an isosceles trapezoid.

Therefore it follows that BG1=CG2.

∴AB2+BD2=AC2+CD2.

Hence it follows that AB⋅BD=AC⋅CD.

Therefore the sets {AB,BD} and {AC,CD} are the same (since they are both equal to the set of roots of the same polynomial).

Note that if AB=CD then AC=BD and then AB+AC=BC, a contradiction.

∴AB=AC.