Question

If 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°.

Answer 1

isocolese triangle has 2 angles of same length

all angles in a triangle add to 180

so
if the angles are m∠A, m∠B, m∠C, then
either m∠A=m∠B or m∠B=m∠C or m∠A=m∠C

anyway

so if we assume that vertex B is the one that has a twin then
130+130+?=180
260+?=180
?=-80
false, we can't have a negative angle measure

so 130 must be the odd one

?+?+130=180
2?+130=180
2?=50
?=25

so
m∠A=m∠C=25°

let's test the 2nd answer choice
m∠A+m∠B=25+130=155, yep

test 3rd
m∠A+m∠C=25+25=50≠60, nope
not 3rd one



so answer is 2nd statement
m∠A + m∠B = 155°

Answer 2

The statement which must be true for an isoscelles triangle ABC has a 130° angle at vertex B is; m∠A + m∠C = 50°.

Triangles

By convention, the sum of angles in a triangle = 180°.

On this note, since the angle at vertex B = 130°.

We can therefore conclude that the algebraic sum of angles at vertex A and C be equal to;

• 180 - 130

Therefore, m∠A + m∠C = 50°.

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