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
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 

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°

(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.

congruent triangles by SAS

ㄥB and ㄥG are corresponding angles

(i) Corresponding Congruent Sides
\(\overline{A B}=\overline{D E} \)
\(\overline{A C}=\overline{D F} \)
\(\overline{B C}=\overline{E F} \)
(ii) Corresponding Congruent Angles
\(\angle A=\angle D \)
\(\angle B=\angle E \)
\(\angle C=\angle F \)

In△XYZ ,∠Y = 72°
∠X:∠Z = 5:4
Let ∠X = 5x, ∠Z = 4x
∠x + ∠y + ∠z = 180°
5x + 4x + 72° = 180°
9x + 72° = 180°
9x = 180^o - 72^o = 108^o
\(x=\frac{108^{\circ}}{9}=12^{\circ}\)
∠X = 5x = 5 x 12 = 60°
∠X = 60°
∠Z = 4x = 4 x 12 = 48°
∠Z = 48°
∠X = 60° ; ∠Z = 48°

\(\angle A+\angle N+\angle G+\angle L+\angle E+\angle S\)
\(=\underbrace{\angle A+\angle E+\angle G}_{\text {Sum of three angles of } \Delta}+\underbrace{\angle S+\angle N+\angle L}_{\text {Sttm of three angles of } \Delta}\)
= 180^o + 180^o = 360^o