Question

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

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

Step-by-step explanation:

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°