Question

An isosceles triangle has an angle that measures 74°. Which other angles could be in that isosceles triangle?

Answer 1

Angle A=74

=>Angle B = C=2x

=> A+B+C=180

=>74+2X=180

=>2x=180-74

=>2x=106

=>x =106/2

=>Angle B,C=53 degrees

Answer 2

GIVEN,

an angle of an isosceles triangle is 74°.

TO FIND,

what could be the other angles.

SOLUTION,

there could be two cases in the given condition.

i) 74° is one of congruent base angles.

∴ we know that tringle has a total of 180°

here according to the condition,

74°+ 74° + x = 180

⇒ 148°+ x= 180

solving,

x= 180-148

x=32°

ii)74° is the vertex angle

here according to the problem,

⇒74° + 2x = 180

⇒2x= 180-74

⇒2x= 106°

⇒x= $\frac{106}{2}$

∴ x= 53°

HENCE THE ANGLES COULD BE 74°, 74°, 32° AND 74°, 53°,53°.