Exterior angle = sum of two interior opposite angles
6y + 2 = 26⁰ + 36⁰
6y + 2 = 62⁰
Subtract 2 from both sides
6y = 62 − 2
6y = 60⁰
\(\frac { 6y }{ 6 } =\frac { 60 }{ 6 } \) [on both sides, divide by 6]
y = 10⁰
ㄥUWY = 6y + 2 = 6(10) + 2 = 62⁰ .
We can conclude that ㄥXWV = ㄥUWY, because they are vertically opposite angles as well as exterior angles.

Exterior angle = sum of two interior opposite angles
128⁰ = x + x
128 = 2x
\(\frac { 128 }{ 2 } =\frac { 2x }{ 2 } \) [on both sides, divide by 2]
x = 64⁰

Exterior angle = sum of two interior opposite angles
135⁰ = z + 40⁰
Subtract 40⁰ on both sides
135⁰ − 40⁰ = z + 40⁰ − 40⁰
z = 95⁰
 

Let, ㄥNMO = y
Exterior angle = sum of two interior opposite angles
y = 62⁰ + 31⁰
= 93⁰ 

Let, ㄥSRQ = x
Exterior angle = sum of two interior opposite angles
x = 38⁰ + 44⁰ = 82⁰

Given angles are 65⁰ and 35⁰.
Let the third angle be x
65⁰ + 35⁰ + x = 180⁰
100⁰ + x = 180°
x = 180⁰ – 100⁰
x = 80⁰

Given, ㄥSUT = 70⁰
ㄥUST = ㄥSTU = x [Angles opposite to equal sides]
ㄥSUT + ㄥUST + ㄥSTU = 180⁰
70⁰ + x + x = 180⁰
70⁰ + 2x = 180⁰
2x = 180⁰ – 70⁰
2x = 110⁰
x = \(\frac { { 110 }^{ 0 } }{ 2 } \) = 55°

Let ㄥA = x
We know that, ㄥA + ㄥB + ㄥC = 180⁰ (angle sum property)
x + 44⁰ + 31⁰ = 180⁰
x + 75⁰ = 180⁰
x = 180⁰ – 75⁰
x = 105⁰

(i) Given angles 80⁰, 70⁰, 50⁰
Sum of the angles = 80⁰ + 70⁰ + 50⁰ = 200⁰ ≠ 180⁰
The given angles cannot form a triangle.
(ii) Given angles 56⁰, 64⁰, 60⁰
Sum of the angles = 56⁰+ 64⁰+ 60⁰ = 180⁰
The given angles can form a triangle.