Question

find the value of angles in the following figure​

Answer 1

$\huge\mathbb{\purple{ANSWER}}$

❒BY EXTERIOR ANGLE SUM PROPERTY↷↷↷

Defination:(An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.)

$↬ (5x + 10) + 58 = 11x + 2 \\ ↬ 5x + 10 + 58 = 11x + 2 \\ ↬ 68 - 2 = 11x - 5x \\ ↬ 66 = 6x \\ ↬ \frac{66}{6} = x \\ ↬ 11 = x$

Put value of X=11° in equations provided in the question

$⇝ 5x + 10 \\ ⇝ 5(11) + 10 \\ ⇝ 55 + 10 \\ ⇝ 60 \\ \\ ⇝ 11x + 2 \\ ⇝ 11(11) + 2 \\ ⇝ 121 + 2 \\ ⇝ 123$

❒VERIFICATION

11x+2=(5x+10)+58

put value of x in this equation

⇛11×11+2=(5×11+10)+58

⇛11×11+2=(55+10)+58

⇛121+2=(55+10)+58

⇛121+2=(65)+58

⇛121+2=65+58

⇛123=65+58

⇛123=123

LHS = RHS

Hence verified!

❒FINAL ANSWER

• Angle TUA = 11x + 2
• Angle TUA = 11 × 11 + 2
• Angle TUA = 121 + 2
• Angle TUA = 123°

• Angle UTS = 5x + 10
• Angle UTS = 5 × 11 + 10
• Angle UTS = 55 + 10
• Angle UTS = 65°

$\huge\mathbb{\pink{❦ジャクソンそしてハン}}$

Answer 2

$\sf\huge \red{Required \:Solution}$

We know:

$\bigstar \boxed{ \rm{}Exterior~angle = Sum~of \: interior ~ angles }$

$\boldsymbol{so:}$

$\leadsto \sf11x + 2 = (5x + 10 )+ 58$

$\leadsto \sf11x + 2 = 5x + 10 + 58$

$\leadsto \sf11x + 2 = 5x + 68$

$\leadsto \sf11x - 5x+ 2 =+ 68$

$\leadsto \sf11x - 5x =+ 68 - 2$

$\leadsto \sf11x - 5x =66$

$\leadsto \sf6x =66$

$\leadsto \sf{}x =\dfrac{66}{6}$

$\leadsto \sf{}x =\dfrac{6 \times 11}{6}$

$\leadsto \sf{}x =\dfrac{\cancel6 \times 11}{\cancel6}$

$\leadsto \sf{}x =\dfrac{1 \times 11}{1}$

$\leadsto \sf{}x =1 \times 11$

$\leadsto \underline{\boxed{\sf{} x =11}}$

$\boldsymbol{verification:}$

$\leadsto \sf11x + 2 = (5x + 10 )+ 58$

put value of x in this equation

$\leadsto \sf11 \times 11+ 2 = (5 \times 11 + 10 )+ 58$

$\leadsto \sf11 \times 11+ 2 = (55+ 10 )+ 58$

$\leadsto \sf121+ 2 = (55+ 10 )+ 58$

$\leadsto \sf121+ 2 = (65 )+ 58$

$\leadsto \sf121+ 2 =65+ 58$

$\leadsto \sf123=65+ 58$

$\leadsto \sf123=123$

LHS = RHS

Hence verified!

• Angle TUA = 11x + 2
• Angle TUA = 11 × 11 + 2
• Angle TUA = 121 + 2
• Angle TUA = 123°

• Angle UTS = 5x + 10
• Angle UTS = 5 × 11 + 10
• Angle UTS = 55 + 10
• Angle UTS = 65°