Question

In triangle ABC angle A is 30 degree and angle B is 60 degree then find angle C​

Answer 1

Question

In triangle ABC angle A is 30 degree and angle B is 60 degree then find angle C

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Required Answer

• $\sf{90^{\circ}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Given

• ${\angle}$A=30 degrees
• ${\angle}$B=60 degrees

$\begin{gathered} \\ {\rule{200pt}{3pt}} \end{gathered}$

To Find

• ${\angle}$C=?

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

Property Used

${\large{\underline{\pmb{\frak{Angle\:Sum\:Property}}}}}$

• Angle sum propety of triangle says that sum of all angles in any triangle will always equal to ${\sf{180^{\circ}}}$.
• $\sf{\:\therefore \red{\angle A+\angle B+\angle C=180^{\circ}}}$

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$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

${\large{\underline{\pmb{\frak{Calculating \:\angle C}}}}}$

${}$

${\qquad{\qquad{\quad{\sf{\large{\longmapsto \angle A+\angle B+\angle C=180^{\circ}}}}}}}$

${}$

${\qquad{\qquad{\quad{\sf{\large{\longmapsto30+60+\angle C=180^{\circ}}}}}}}$

${}$

${\qquad{\qquad{\quad{\sf{\large{\longmapsto 90+\angle C=180^{\circ}}}}}}}$

${}$

${\qquad{\qquad{\quad{\sf{\large{\longmapsto \angle C=180-90}}}}}}$

${}$

${\qquad{\qquad{\quad{\therefore{\underline{\boxed{\sf{\purple{\normalsize{\angle C=90^{\circ}}}}}}}}}}}$

${}$

$\begin{gathered} \\ \qquad{\rule{150pt}{1pt}} \end{gathered}$

$\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}} \end{gathered}$

~Therefore

• ${\angle}$C is equal to $\sf{90^{\circ}}$

$\begin{gathered} \\ {\underline{\rule{200pt}{7pt}}} \end{gathered}$