question_answer

Find the value of unknown x in the following diagrams:

(a)

(b)

(c)

(d)

Answer:

(a) The sum of interior angles of a triangle is\[180{}^\circ \]

\[\therefore \]      \[\angle A+\angle B+\angle C=180{}^\circ \]

\[x+50{}^\circ +60{}^\circ =180{}^\circ \]

\[x+110{}^\circ =180{}^\circ \]

\[x={{180}^{\circ }}-{{110}^{\circ }}={{70}^{\circ }}\]

(b) The sum of interior angles of a triangle is\[180{}^\circ \]

\[\therefore \]     \[\angle P+\angle Q+\angle R=180{}^\circ \]

\[90{}^\circ +30{}^\circ +x{}^\circ =180{}^\circ \]

\[120{}^\circ +x{}^\circ =180{}^\circ \]

\[{{x}^{\circ }}={{180}^{\circ }}-{{120}^{\circ }}\]

\[x{}^\circ =60{}^\circ \]

(c) The sum of interior angles of a triangle is\[180{}^\circ \]

\[\angle X+\angle Y\text{+}\angle Z=180{}^\circ \]

\[30{}^\circ +110{}^\circ +x{}^\circ =180{}^\circ \]

\[140{}^\circ +x{}^\circ =180{}^\circ \]

\[x{}^\circ =180{}^\circ -140{}^\circ \]

\[x{}^\circ =40{}^\circ \]

(d) Since, the sum of all 3 interior angles of a triangle is \[180{}^\circ \].

\[\therefore \]      \[50{}^\circ +x{}^\circ +x{}^\circ =180{}^\circ \]

\[50{}^\circ +2x{}^\circ =180{}^\circ \]

\[2x{}^\circ =180{}^\circ -50{}^\circ \]

\[2x{}^\circ =130{}^\circ \]

\[x{}^\circ =\frac{130{}^\circ }{2}\]

\[x{}^\circ =65{}^\circ \]