Download App

The Triangle and Its Properties — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSThe Triangle and Its Properties5 Marks
Question
Find angle x in each figure.
Image
✓

Answer

(i)
Image
Let the given triangle be $\triangle A B C$, then we have $A B=A C$. We know that angle opposite to equal sides of an isosceles triangle are equal.
$\therefore \quad x=40^{\circ}$
Hence, the value of $x$ is $40^{\circ}$.
(ii)
Image
Let the given triangle be $\triangle A B C$. Then, we have $A B=A C$.
So, $\triangle A B C$ is an isosceles triangle.
$\therefore \angle A=\angle C=45^{\circ}$
[since, the angle opposite to equal sides of an isosceles triangle are equal]
Now, in $\triangle A B C$ by angle sum property of a triangle,
$\angle A+\angle B+\angle C=180^{\circ} \Rightarrow 45^{\circ}+x+45^{\circ}=180^{\circ} $
${[\angle A=\angle B=45 \text { because of equal side}]}$
$\Rightarrow \quad x+90^{\circ}=180^{\circ} \Rightarrow x=180^{\circ}-90^{\circ}=90^{\circ}$
Hence, the value of $x$ is $90^{\circ}$.
(iii) Ans. $x=50^{\circ}$
(iv) Ans. $x=40^{\circ}$
(v) Ans. $45^{\circ}$
(vi) Ans. $x=70^{\circ}$
(vii)
Image
Let the given triangle be $\triangle A B C$.
Then, we have
$A B=A C$
So, $\triangle A B C$ is an isosceles triangle.
$\therefore \quad \angle A C B=\angle B$
[since, the angle opposite to equal sides of an isosceles triangle are equal]
$\angle A C B=x$
We know that linear pair of angles is supplementry.
$\therefore \angle A C B+\angle A C D=180^{\circ} \quad \text { [linear pair] } $
$\Rightarrow x+120^{\circ}=180^{\circ} {[\because \angle A C D=120, \text { given] }} $
$\Rightarrow x=180^{\circ}-120^{\circ}=60^{\circ}$
Hence, the value of $x$ is $60^{\circ}$.
(viii)
Image
Let the given triangle be $\triangle A B C$. Then, we have
$A B=A C$
So, $\triangle A B C$ is an isosceles triangle.
$\therefore \quad \angle B=\angle C$
[since, the angle opposite to equal sides of an isosceles triangle are equal]
Also, $\angle D A C$ is an exterior angle of $\triangle A B C$.
Now, by exterior angle property of a triangle,
Sum of two interior opposite angles = Exterior angle
$\Rightarrow x+x=110^{\circ} \Rightarrow 2 x=110^{\circ}=\frac{110^{\circ}}{2}=55^{\circ}$
Hence, the value of $x$ is $55^{\circ}$.
(ix)
Image
Let given triangle be $\triangle A B C$. Then, we have $A B=B C$ So, $\triangle A B C$ is an isosceles triangle.
$\therefore \quad \angle B A C=\angle B C A=x$
From the figure,
$\angle B C A=\angle D C E=30^{\circ} \text { [vertically opposite angles] }$
From Eq. (i), $\angle B A C=\angle B C A$
$\Rightarrow \quad x=30^{\circ}$
Hence, the value of $x$ is $30^{\circ}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from The Triangle and Its Properties→The Triangle and Its Properties — all question types→MATHS STD 7 question papers→Gujarat Board STD 7 question papers→Gujarat Board question paper generator→

Similar questions

A path $5 \ m$ wide runs along inside a square park of side $100 \ m$. Find the area of the path. Also find the cost of cementing it at the rate of ₹ $250 ~per ~10 ~m^2$.
→
In Fig.$A B \| C D$ and $A E \| C F ; \angle F C G=90^{\circ}$ and $\angle B A C=120^{\circ}$. Find the values of $x, y$ and $z$.
Image
→
Explain the concept of interior and exterior angle and in the figures given below. Find $x$ and $y.$
→
The following data gives the amount of manure $($in thousand tonnes$)$ manufactured by a company during some years:
Year $1992$ $1993$ $1994$ $1995$ $1996$ $1997$
Manure $($in thousand tonnes$)$ $15$ $35$ $45$ $30$ $40$ $20$
Represent the above data with the help of a bar graph.
$1.$ Indicate with the help of the bar graph the year in which the amount of manure manufactured by the company was maximum.
$2.$ Choose the correct alternative:
The consecutive years during which there was maximum decrease in manure production are:
→
$\frac{\text{x}}{2}+\frac32=\frac{2\text{x}}{5}-1$
→
If $P=7 x^2+5 x y-9 y^2, Q=4 y^2-3 x^2-6 x y$ and $R=-4 x^2+x y+5 y^2$, show that $P+Q+R=0$.
→
Various modes of transport used by $1850$ students of a school are given below:
School bus
Private bus
Bicycle
Rickshaw
By foot
$640$
$360$
$490$
$210$
 $150$
Draw a bar graph to represent the above data.
→
The daily wages (in ₹) of 15 workers in a factory are given below:
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180
Prepare the frequency table and find the mean wage.
→
A wall is $4.5m$ long and $3m$ high. It has two equal windows, each having form and dimensions as shown in Figure. below. Find the cost of painting the wall (leaving windows) at the rate of $Rs. 15$ per $m^2$.
→
Observe the following table and complete it.
StatementInference
(- 8) $\div$ (- 4) = 2Result is an integer
(- 4) $\div$ (- 8) = $\frac{- 4}{- 8}$Result is not an integer
(- 8) $\div$ 3 = $\frac{-8}{3}$ 
3 $\div$ (- 8) = $\frac{3}{-8}$ 
→