Question

Find the unknown angles ​

Answer 1

Solution 1) ( figure 1 ) :

Let us name the angle adjacent to angle a as angle m . Then ,

m = 70° , because they are both the base angles opposite to each other of an isosceles triangle and the base angles opposite to each other in an isosceles triangle will always be equal .

Hence , angle m = 70°

Let us name the angle adjacent to angle b as angle n , then according to the angle sum property ,

70° + 70° + n = 180°

140° + n = 180°

n = 180° - 140° = 40°

n = 40°

Angle a and angle m are a linear pair which means that they will sum up to 180°

Hence 70° + a = 180°

a = 180° - 70°

[ a = 110° ]

angle b and angle n are a linear pair which means that they will sum up to 180° .

Hence , 40° + b = 180°

b = 180° - 40°

[ b = 140° ]

Therefore the unknown angle a = 110° and the unknown angle b = 140°

Solution 2) ( figure 2 ) :

Let us name the angle adjacent to angle y as angle w .

angle 23° + angle 89° + angle w = 180°

23°+ 89°+ w = 180°

112° + w = 180°

w = 180° - 112°

w = 67°

angle 23° and angle 89° are the interior opposite angles of angle y which means that their sum will add up to angle y .

= 23° + 89° = y

= y = 112°

[ y = 112° ]

angle x and angle y are corresponding angles which means that their measure will be equal .

Hence x = y = 112°

x = 112°

[ x = 112° ]

Therefore , the unknown angle y = 112° and the unknown angle x = 112° .

Hope you find my answer useful!!!

Answer 2

a= 110.....b=140.........