Question

in figure 9.9 TQ and TR are the bisectors of angle Q and angle R respectively if angle QPR equals to 80 degree and Angle PRT equals to 30 degree , determine angle TQR angle and angle QTR.

Answer 1

$\textbf{\huge{\underline{ Hello Mate! }}}$

Since the two lines are bisectors,

< QTR = 90° + 1 < QPR / 2

< QTR = 90° + ( 1 / 2 × 80° )

< QTR = 90° + 40°

< QTR = 130°

$\textsf{\red{ Hence angle QTR is 130° }}$

Since TR is bisector,

< TRQ = 30°

< TRQ + < QTR + < TQR = 180° ( Angle sum property )

30° + 130° + < TQR = 180°

< TQR = 20°

$\textsf{\blue{ Hence angle TQR is 20° }}$

$\textbf{ Have great future ahead! }$

Answer 2

❤$\huge{\ulcorner{\pink{Hlw\: mate}}}\rfloor$❤

$\green{Here's\: ur\: answer..!!}$

$<b><i>To determine the values of ◆TQR◆ and◆ QTR◆<b><i>$

Given that...,,
<P=80°
<TRP=30°
..
first of all let's find..
<QTR

<QTR=90°+(1/2×80°)
<QTR=90°+40°

$\purple{QTR=130°}$

Now by angle sum property of a triangle
<QTR+<TRQ<TQR=180°

•°• 130° + 30° +<TQR=180°

$\orange{TQR=20°}$

$\huge\red{Thanks!!!}$