SChand Composite Mathematics Class 7 Chapter 11 Triangle and it's Properties Exercise 11B

 Exercise 11B 

Question 1 

Find the lettered angle in each case: 

(i)(IMAGE TO BE ADDED)

Sol: $\Rightarrow x+30^{\circ}=70^{\circ}$

$\Rightarrow x=70-30^{\circ}$

$\Rightarrow x=40^{\circ}$

(ii) (IMAGE TO BE ADDED)

Sol: 

$\begin{aligned} \angle a &=35^{\circ}+50^{\circ} \\ \angle a &=85^{\circ} \end{aligned}$

(iii)  (IMAGE TO BE ADDED)

Sol: $\angle y=30+45$

$\angle y=75^{\circ}$

(iv)  (IMAGE TO BE ADDED)

Sol: $\Rightarrow 100^{\circ}=x+70^{\circ}$

$\Rightarrow x=100-70$

$\Rightarrow x=30^{\circ}$

Question 2

Find the lettered angle in each case: 

(IMAGE TO BE ADDED)

(i) By l.p    y+ $120^{\circ}=180^{\circ}$

$y=180^{\circ}-120^{\circ}$

$y=60^{\circ}$ Ans

$x=40+60 \Rightarrow y=100^{\circ}$

(ii) (IMAGE TO BE ADDED)

Sol: $\triangle A P  B \quad \angle P+\angle P A B+\angle P B A=180^{\circ}$

$\Rightarrow \quad \angle P B A+50^{\circ}+100^{\circ}=130^{\circ}$

$\Rightarrow \angle P B A=130^{\circ}-150^{\circ}$

$\Rightarrow \angle P B A=30^{\circ}$ Ans

$\Rightarrow \dot{y}=50^{\circ}+2 \Rightarrow y=50+30$

$\Rightarrow y=80^{\circ}$ Ans

$\Rightarrow x+y+75^{\circ}=180^{\circ} \Rightarrow x+80^{\circ}+75^{\circ}=180^{\circ}$

$\Rightarrow x=180^{\circ}-155^{\circ} \Rightarrow x=25^{\circ} \Rightarrow \mathrm{Ans}$

(iii)  (IMAGE TO BE ADDED)

$x=70^{\circ}$ [Vertically]

$x+y=110^{\circ}$ $\Rightarrow y=110^{\circ}-70^{\circ} \Rightarrow y=40^{\circ}$

$\Rightarrow \quad x+y+z=180^{\circ}$

$\Rightarrow 70^{\circ}+40^{\circ}+2=180^{\circ} \Rightarrow z=180^{\circ}-110^{\circ} \Rightarrow 2=70^{\circ}$

(iv) (IMAGE TO BE ADDED)

 $90^{\circ}=50^{\circ}+y$

$\Rightarrow y=90^{\circ}-50^{\circ} \Rightarrow y=40^{\circ}$

$\triangle D E C$

$\begin{aligned} 100+40 &+x=180^{\circ} \\ x &=180-140 \\ x &=40^{\circ} \mathrm{Ans} \end{aligned}$

Question 3

One of the exterior angles of a triangle is 100 degree and its interior opposite angles are equal to each other . what is the measure of each of these two angles? 

Sol: Let angles =x 

$\Rightarrow x+x=100 \Rightarrow 2 x=100 \Rightarrow x=50^{\circ}$

Question 4

One of the exterior angle of a triangle is $130^{\circ}$ and the interior opposite angles are in the ratio 2: 3 . find the angles of the triangle . 

Sol: $2 x+3 x=130^{\circ} \quad \Rightarrow 5 x=130^{\circ}$

$\Rightarrow x=\frac{130}{5} \quad \Rightarrow \quad x=26^{\circ}$

$\Rightarrow 2 x=2 \times 26=52^{\circ}$ Ans $; \quad 3 x=3 \times 26=78^{\circ}$ Ans 

Question 5

Find the value of x in each case: 

(IMAGE TO BE ADDED)

Sol: $\triangle A B C$

$60+45^{\circ}+\angle C=180^{\circ}$

$\angle C=180^{\circ}-105^{\circ}$

$\angle C=75^{\circ}$ Ans 

$\triangle C E D$

$\begin{aligned} & 80+75+x=180^{\circ} \\ \Rightarrow & x=180^{\circ}-155^{\circ} \Rightarrow x=25^{\circ} \end{aligned}$

(ii)  (IMAGE TO BE ADDED) 

Sol: Ex= Int opp + int opp

$\Rightarrow 11 x-60^{\circ}=3 x+40^{\circ}+4 x$

$\Rightarrow 11 x-60^{\circ}=7 x+40^{\circ}$

$\Rightarrow 11 x-7 x=60^{\circ}+40^{\circ}$

$4 x=100^{\circ}=x \cdot x=\frac{100}{4}$

$x=25^{\circ}$ Ans 

(iii)  (IMAGE TO BE ADDED) 

By L.P 

$\Rightarrow 100+y=180^{\circ}$

$\Rightarrow y=180^{\circ}-100^{\circ}$

$\Rightarrow y=80^{\circ}$ Ans 

$\Rightarrow y+3 x^{\circ}=7 x^{\circ}$

$\Rightarrow 30^{\circ}=7 x-3 x \Rightarrow 4 x=30^{\circ}$

x = $20^{\circ}$ Answer 

(iv)  (IMAGE TO BE ADDED

Sol: $\angle P T Q=\angle T Q R+\angle Q R T$

 $90^{\circ}=48^{\circ}+\angle Q R T$

$\Rightarrow \quad \angle Q R T=90-48^{\circ}$

$\Rightarrow \angle Q R T=42^{\circ}$

$\triangle P S R \rightarrow$

$x=\angle S P R+\angle S R P$

$x=30^{\circ}+42^{\circ}$

$x=72^{\circ}$ Ans