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2023-II-22

Posted on 25-07-2023 By app.cch No Comments on 2023-II-22
Ans: B

Let $\angle TSU =x$. In $\Delta STU$, we have

$\begin{array}{rcll}
ST & = & TU & \text{(given)} \\
\angle TUS & = & \angle TSU & \text{(base $\angle$s, isos. $\Delta$)} \\
\angle TUS & = & x
\end{array}$

In $\Delta SUV$,

$\begin{array}{rcll}
\angle RSU & = & \angle SUV +\angle SVU & \text{(ext. $\angle$ of $\Delta$)} \\
\angle RSU & = & x+48^\circ
\end{array}$

In $\Delta SUW$,

$\begin{array}{rcll}
\angle RUS & = & \angle SWU +\angle USW & \text{(ext. $\angle$ of $\Delta$)} \\
\angle RUS & = & 32^\circ +x
\end{array}$

Since $RSTU$ is a cyclic quadrilateral, we have

$\begin{array}{rcll}
\angle RUT +\angle RST & = & 180^\circ & \text{(opp. $\angle$s, cyclic quad.)} \\
\angle RUS+\angle SUT +\angle RSU +\angle UST & = & 180^\circ \\
32^\circ +x+x+x+48^\circ+x & = & 180^\circ \\
4x & = & 100^\circ \\
x & = & 25^\circ
\end{array}$

Hence, we have

$\begin{array}{rcl}
\angle RSU & = & 25^\circ+48^\circ \\
\angle RSU & = & 73^\circ
\end{array}$

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2023, HKDSE-MATH, Paper 2 Tags:Properties of Circles

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3D Problems (41) Basic Functions (13) Basic Geometry (68) Binomial Theorem (7) Change of Subject (32) Complex Numbers (16) Coordinates (46) Differentiation (16) Equations of Circle (54) Equations of Straight Line (43) Estimations and Errors (35) Factorization (39) Graph of Functions (3) Inequality (39) Integration (15) Laws of Indices (43) Linear Programming (21) Locus (13) Logarithm (34) Mathematical Induction (7) Matrices (4) Mensuration (98) Numeral System (19) Percentage (42) Polynomials (49) Probability (85) Properties of Circles (56) Quadratic Equations and Functions (57) Rate and Ratio (30) Rational Functions (20) Sequences (66) Simultaneous Linear Equations (27) Statistics (122) System of Linear Equations (3) Transformations (44) Trigonometry (M2) (7) Trigonometry and Its Applications (67) Variations (38) Vectors (3)

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