Question

Calculate the angles of a triangle if they are in the ratio 4:5:6

Answer 1

• As per the data given in the question, we have to find the value of the expression.

            Given data:- Ratio of the triangle $4:5:6.$

            To find:- Calculate angles of the triangle.

            Solution:-

• We know that triangle has three angles and three sides.

• In a triangle, the sum of angles of a triangle is $180$°.

         $\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}=180^{\circ}$

         It is given that

        $\angle \mathrm{A}: \angle \mathrm{B}: \angle \mathrm{C}=4: 5: 6\\\text { Consider } \angle \mathrm{A}=4 \mathrm{x}, \angle \mathrm{B}=5 \mathrm{x} \text { and } \angle \mathrm{C}=6 \mathrm{x}$

        Substituting the values

        $4 \mathrm{x}+5 \mathrm{x}+6 \mathrm{x}=180^{\circ}$

        By further calculation

         $\begin{array}{l}15 \mathrm{x}=180^{\circ} \\\mathrm{x}= \frac{180^{\circ}}{15} =12\end{array}$

        $\begin{array}{l}\angle \mathrm{A}=4 \mathrm{x}=4 \times 12^{\circ}=48^{\circ} \\\angle \mathrm{B}=5 \mathrm{x}=5 \times 12^{\circ}=60^{\circ} \\\angle \mathrm{C}=6 \mathrm{x}=6 \times 12^{\circ}=72^{\circ}\end{array}$

         Hence we will get the angles $48^{\circ} ,60^{\circ} ,72^{\circ}.$