EXERCISE 17 A

1.The three angles of a triangle measures (2x-10degree) , (x+31deg) and (5x+7deg) . Find the value of x and hence all the angles of the triangle

2.One of the exterior angles of a triangle is 153 deg and the interior opposite angles are in the ratio 5 : 4 . Find the three interior angles of the triangle.

3.If the three angles of a triangle are (x+15deg) , (\dfrac{6x}{5}+6 deg) and (\dfrac{2x}{3}+30 deg) , prove that the triangles is an equilateral triangles.

4.Find the value of x and y in the following figures:

(i)

(ii)

5.In the given figure, angleA = 54 deg , BO and CO are the bisectors of angleB and angle C . Find angleBOC [Hint: in deltaABC , 2x+2y+54 deg=180 deg\rightarrow 2(x+y)=126deg\\x+y=63 deg

In deltaBOC , x+y+z=180 deg]

6.In an isosceles triangle each base angle is 30 deg greater than the vertical angle . Find the measure of all the three angles of the triangles .

7.In the figure given below AN=AC , angleBAC=52 deg , angleACK=84 deg , and BCK is a straight line. Prove that NB = NC

8.In the figure AB=AC . Prove that BD=BC

9.The ratio between the vertical angle and base angle of an isosceles triangle is 2 : 5. Find the angles of the triangle.

[Hint: $\dfrac{vertical~angle}{base~angle}=\dfrac{2}{5}, i.e., \dfrac{v}{b}=\dfrac{2}{5}\rightarrow v=\dfrac{2}{5}b$ (v denotes vertical angle and b denotes base angle)

Now , v+b+b=180 deg \rightarrow \dfrac{2}{5}b+b+b=180deg]

10.Prove that the sum of the exterior angles of a triangle taken in order is 360°. i.e., x + y + z = 360°.

[Hint: Let int. angleA = a° , int angleB = b°, int.angleC=c° \rightarrow a a + b + c = 180°

By ext. angleProperty x=a+b , y=b+c , z=a+c

x+y+z=a+b+b+c+a+c=2(a+b+c].

11.Find the lettered angles in each of the followlng figures-

(i)

(ii)

(iii)

(iv)

(v)

(vi)

12.In the adjoining figure, AE||BC. With the help of the given information find the value of x and y

[Hint: angleDAE=angleABC \rightarrow x+19=y-11\rightarrow x-y=-30 ….(i)

2x+y+y-11+x+11=180\rightarrow3x+2y=180 …(ii). Solve (i) and (ii)]