Question
Find the unknown marked angles in the given figure:
✓
Answer
In the figure,
$ x=60^{\circ} $.........(Alternate angles)
Let each equal angle of an isosceles triangle be a
then $a+a+x=180^{\circ}$ ........... (Angles of a triangle)
$ \begin{aligned} & \Rightarrow 2 \mathrm{a}+\mathrm{x}=180^{\circ} \\ & \Rightarrow 2 \mathrm{a}+60^{\circ}=180^{\circ} \\ & \Rightarrow 2 \mathrm{a}=180^{\circ}-60^{\circ}=120^{\circ} \\ & \Rightarrow \mathrm{a}=\frac{120^{\circ}}{2}=60^{\circ} \end{aligned} $
$ \therefore y=x+a=60^{\circ}=120^{\circ} $
Hence $x=60^{\circ}$ and $y=120^{\circ}$
$ x=60^{\circ} $.........(Alternate angles)
Let each equal angle of an isosceles triangle be a
then $a+a+x=180^{\circ}$ ........... (Angles of a triangle)
$ \begin{aligned} & \Rightarrow 2 \mathrm{a}+\mathrm{x}=180^{\circ} \\ & \Rightarrow 2 \mathrm{a}+60^{\circ}=180^{\circ} \\ & \Rightarrow 2 \mathrm{a}=180^{\circ}-60^{\circ}=120^{\circ} \\ & \Rightarrow \mathrm{a}=\frac{120^{\circ}}{2}=60^{\circ} \end{aligned} $
$ \therefore y=x+a=60^{\circ}=120^{\circ} $
Hence $x=60^{\circ}$ and $y=120^{\circ}$
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
Evaluate : $\frac{11}{3}+\frac{-5}{3}+\frac{-2}{3}$
→Divide: $9a^4b - 15a^3b^2 + 12a^2b^3 by - 3a^2b$
→Subtract : $3 a-2 b+4 c$ from $5 a-3 b-5 c$
→In the given figure, the directed lines are parallel to each other. Find the unknown angles.
Evaluate: 16 - 5 × 3 + 4
Cost of $3 \frac{5}{7}$ litres of oil is ₹ $83 \frac{1}{2}$. Find the cost of one-litre oil.
→The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters.
Simplify: $6+\left\{\frac{4}{3}+\left(\frac{3}{4}-\frac{1}{3}\right)\right\}$
→Multiply: $(2x + 3y)(2x - 3y)$
→The price of a fan increases from ₹ 3260 to ₹ 3749. Find the increase per cent in its price.