Question

find the angles marked with letters.for the more difficult questions it is helpful to draw the diagram

only question 13 and 15​

Answer 1

Q.15 Angle sum property of a triangle =

3x + 2x + x = 180

6x = 180

x = 180/6 = 30°

So, Angle 3x = 3 × 30 = 90°

Angle 2x = 2 × 30 = 60°

Angle x = 30°

Answer 2

Answer:

answer for 13th is 154

answer for 15th is :-

x = 30 , 2x = 60 and 3x = 90

Step-by-step explanation:

In ques 13th .. two methods can be taken

first being exterior angle prop. second being angle sum prop . The one which you feel easy you may apply ...

By exterior. angle prop. ...

1. As two short lines are there refering that the two respective sides are equal which is only in case of isosceles triangle . * An important rule for isosceles triangle is that the two lines which are equal there base angles will also be equal * that is why the other interior opposite angle is also 77° .
2. Now , Ext. Angle = sum of interior two opposite angles . Thus , x = 77°+77° (acc. to ext. angle prop.) and hence 77+77 we have 154° .
3. That is why , x = 154°

By angle sum prop. ...

1. As the other angle is of 77° ( reason in detail is mentioned above in 1st point of ext. angle prop. )
2. angle sum prop. - The sum of all angles of ∆ is 180°
3. So , firstly we have to find the third angle ..
4. Let the third angle be *x*
5. So , x + 77° + 77° = 180°(angle sum prop.)
6. so , x + 154 = 180° and then x = 180°- 154° i.e. 26° . Now as we know all three angles so we have to find the ext. angle ..
7. so acc. to supplements or linear pair of angles ( straight angle ) their sum will be 180°
8. Therefore , Let the ext. angle be y.
9. Thus , y+26°=180°( linear pair of angles ) and the answer will be y = 154° .

Hence by both ways answer will come ext. angle or x = 154° but I advice you to use ext. angle prop as it involves just 1 step of solving ..

In ques 15th ...

1. Acc. to angle sum prop ..
2. x + 2x + 3x = 180°
3. 6x = 180°
4. x = 180°/6 = 30°
5. So x = 30° i.e. the first angle ..
6. now the sec. angle is 2x that will be 2×30° = 60° and third angle is 3x that will be 3×30° = 90° ..

Hence the answer is 30°,60°,90° acc. to angle sum prop ...

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