If the isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?
m∠A = 15° and m∠C = 35°
m∠A + m∠B = 155°
m∠A + m∠C = 60°
m∠A = 20° and m∠C = 30°

Solution:

Given, isosceles triangle ABC has a 130° angle at vertex B.

In an isosceles triangle, two angles are exactly equal.

So, angles at Vertex A and Vertex C are equal.

Angle at Vertex A and C be X.

In any triangle, the sum of interior angles is equal to 180°.

So, X + X + 130° = 180°

2X + 130° = 180°

2X = 180° - 130°

2X = 50°

X = 50°/2

X = 25°

Therefore, the angles at vertex A and C are 25° each.

From the option,

1) m∠A = 15° and m∠C = 35°

Since, the given triangle is isosceles, angle A and C must be equal.

Therefore, option(1) is not true

2) m∠A + m∠B = 155°

Given, m∠B = 130°

We know, m∠A = 25°

LHS = m∠A + m∠B

= 25° + 130°

= 155°

RHS = 155°

LHS = RHS

Therefore, option(2) is true.

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If the isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

Summary:

If the isosceles triangle ABC has a 130° angle at vertex B, the statement m∠A + m∠B = 155° is true.