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If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
OmZA = 15° and mZC = 35°
mZA = 25° and mZC = 25°
OmZA = 20° and mZC = 30°
OmZA + m ZB = 155° and mZC = 60°

If isosceles triangle ABC has a 130 angle at vertex B which statement must be true OmZA 15 and mZC 35 mZA 25 and mZC 25 OmZA 20 and mZC 30 OmZA m ZB 155 and mZC class=

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Answer:

m∠A = 25° and m∠C = 25°

Step-by-step explanation:

The sum of all three angles in a triangle must add up to 180°.  Since the measure of angle B is 130°, the sum of the other two angles have to be 50°.  

Also, the triangle is isosceles, meaning two of the sides are equal in length.  For those sides, their corresponding angles must also be equivalent.  In this case, it's the two smaller angles.  Since we have 50° between the two angles, A and C, divide 50 by 2 to get 25° for both angle measurements.  

The statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

Geometry

From the question, we are to determine which of the statements must be true

From the given information,

m ∠B = 130°

Since the triangle is an isosceles triangle, the base angles must be equal

That is,

m ∠A = m ∠C

But, angles in a triangle sum up to 180°

Then,

∠A + ∠B + ∠C = 180°

This becomes

2 × ∠A + 130° = 180°

2 × ∠A = 180° - 130°

2 × ∠A = 50°

∠A = 50° ÷ 2

∠A = 25°

Since ∠A = ∠C

Therefore,

∠C = 25°

Hence, the statement that must be true is m ∠A = 25° and m ∠C = 25°. The correct option is the second option m ∠A = 25° and m ∠C = 25°

Learn more on Geometry here: https://brainly.com/question/14440001

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