Question

one of exterior angle of triangle ABC measures 150 degree one of the opposite interior angle is 75° find the other interior opposite angle what type of triangle is this​

Answer 1

Answer: 75 , Isosceles

Step-by-step explanation: Exterior angle = sum of opposite interior angles

So let the other opposite interior angle be 'x'

x + 75 = 150

x = 150-75

x = 75 degrees

let the other angle be x

Angle sum property of a triangle is 180 degrees

x + 75 + 75 = 180

x + 150 = 180

x = 180-150 =30 degrees

Therefore, This triangle is an isosceles triangle

Answer 2

Answer:

Given - exterior angle = 150 °

one opposite interior angle = 75 °

to find = other two interior angle

proof = we know that sum of two opposite interior angle is exterior angle of third

then ,

let the other opposite interior angle is x

75° + x = 150 °

x = 150 ° - 75 °

x = 75°

thus , the other opposite angle = 75°

now , we have two angles which are 75° , 75° respectively

now , we can by third angle

let the third angle be y

75° + 75° + y = 180° ( angle sum property )

150 ° + y = 180 °

y = 180° - 150°

y = 30 °

all the three angles are 70° , 70° , 30°

this is an isoscales triangle because its two sides are equal