FINDING MISSING ANGLES IN TRAINGLES WORKSHEET

Find the missing angle in a the triangles given below.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Problem 1 :

Solution :

<A+<B+<C  =  180

Given <A  =  x, <B  =  2x and <C  =  90

x+2x+90  =  180

3x+90  =  180

3x  =  180-90

3x  =  90

x  =  90/3

x  =  30

So, <A  =  30 and <B  =  60.

Problem 2 :

<D + <E + F  =  180  ----(1)

Since it is isosceles triangle, <E  =  <F and <D  =  90

Let <E  =  x

90 + x + x  =  180

2x+90  =  180

Subtracting 90 on both sides, we get

2x  =  90

Divide by 2 on both sides, we get

x  =  90/2

x  =  45

Problem 3 :

Solution :

<T  =  42, <U  =  42, <V  =  ?

<U + <V + <T  =  180

42 + <V + 42  =  180

<V + 84  =  180

Subtracting by 84 on both sides, we get

<V  =  96

Problem 4 :

Solution :

Vertically opposite angles are equal. So <2  =  40.

<1 + 40 + 90  =  180

<1 + 130  =  180

<1  =  50

<3 + <2 + 95  =  180

<3+40  =  180

<3  =  140

Problem 5 :

Solution :

In small triangle the indicated angle is 90 degree.

Using exterior angle theorem,

56+45  =  50 + <2

<2  =  101-50

<2  =  51

<1 + <2 + 50  =  180

<1+51+50  =  180

<1+101 =  180

<1  =  180-101

<1  =  79

In small triangle,

<2+<3+90  =  180

51 + <3 + 90  =  180

<3  =  180-141

<3  =  39

Problem 6 :

Solution :

By using exterior angle theorem,

x+31  =  2x-8

2x - x  = 31 + 8

x  =  39

Problem 7 :

Solution :

Using exterior angle theorem,

10x+9  =  7x+1+38

10x-7x  =  39 - 9

3x  =  30

x  =  10

Question 8 :

Solution :

Sum of interior angles of a triangle

x + 2x-21 + 90  =  180

3x+69  =  180

Subtracting 69 on both sides, we get

3x  =  180-69

3x  =  111

Dividing by 3 on both sides, we get

x  =  111/3

x  =  37

Question 9 :

Solution :

Sum of interior angle of triangle  =  180

x+x+72  =  180

Subtracting 72 on both sides

2x  =  180-72

2x  =  108

Dividing by 2 on both sides

x  =  54

Question 10 :

Solution :

Since it is isosceles triangle, the angle formed by equal sides will be equal.

x+35+35  =  180

x+70  =  180

Subtracting 70 on both sides

x  =  180-70

x  =  110

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