Question
Find the interior angles of the following triangles:
✓
Answer
In $\triangle ACD,$
$AD = CD ....($given$)$
$\Rightarrow \angle ACD = \angle CAD ....($angles opposite to two equal sides are equal$)$
Now, $\angle ACD = 50^\circ ....($given$)$
$\Rightarrow \angle CAD = 50^\circ $
By exterior angle property,
$\angle ADB = \angle ACD + \angle CAD = 50^\circ + 50^\circ = 100^\circ $
In $\text{ADB},$
$AD = BD ....($given$)$
$\Rightarrow \angle DBA =\angle DAB ....($angles opposite to two equal sides are equal$)$
Also, $\angle ADB + \angle DBA + \angle DAB = 180^\circ $
$\Rightarrow 100 + 2\angle DBA = 180^\circ $
$\Rightarrow 2\angle DBA = 80^\circ $
$\Rightarrow \angle DBA = 40 ^\circ $
$\Rightarrow \angle DBA = 40^\circ $
$\angle BAC = \angle DAB + \angle CAD = 40^\circ + 50^\circ = 90^\circ $
Hence, the interior angles of $\triangle ABC$ are $50^\circ , 90^\circ $ and $40^\circ .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $a +\frac{1}{ a }=6$;find $a -\frac{1}{ a }$
→If $\cot \theta=\frac{1}{\sqrt{3}}$, show that $\frac{1-\cos ^2 \theta}{2-\sin ^2 \theta}=\frac{3}{5}$
→Construct a $\triangle PQR$ with $\angle Q = 60^\circ , \angle R = 45^\circ $ and the perpendicular from $P$ to $QR$ be $3.5 \ cm.$ Measure $PQ.$
→Solve the following pairs of equations$:\ \frac{3}{2 x}+\frac{2}{3 y}=5;\frac{5}{x}-\frac{3}{y}=1$
→A shopkeeper allows two successive discounts of $10\%$ and $15\%$ on his articles. If he gets $Rs.2295$ for an article, find its marked price.
→In the given figure, $A D$ is a median of $\triangle A B C$ and $P$ is a point on AC such that :
$\operatorname{ar}(\triangle ADP ): \operatorname{ar}(\triangle ABD )=2: 3$.
Find: (i) $AP : PC$ (ii) ar ( $\triangle PDC$ ) : ar ( $\triangle ABC$ ).
→$\operatorname{ar}(\triangle ADP ): \operatorname{ar}(\triangle ABD )=2: 3$.
Find: (i) $AP : PC$ (ii) ar ( $\triangle PDC$ ) : ar ( $\triangle ABC$ ).
$A$ line segment $AB$ is bisected at point $P$ and through point $P$ another line segment $PQ$, which is perpendicular to $AB$, is drawn. Show that: $QA = QB.$
→In the given figure, $A B \| S Q\| D C$ and $A D \| P R \| B C$. If the area of quadrilateral $\text{ABCD}$ is $24$ square units, find the area of quadrilateral $\text{PQRS}.$
→In a $\|$ gm $A B C D$, it is given that $A B=16 cm$ and the altitudes corresponding to the sides AB and AD are 6 cm and 8 cm respectively.
Find the length of AD .
→Find the length of AD .
Find the amount and the compound interest payable annually on the following :$Rs.25000$ for $1 \frac{1}{2}$years at $10\%$ per annum.
→