Question

Drag an answer to each box to complete this paragraph proof.

Answer 1

(x) + (3x) + (5x) = 180

9x = 180

x = 20

answer

1st box: (x) + (3x) + (5x) = 180

2nd box: x = 20

Answer 2

Answer: For first box - (x)°+(3x)°+(5x)°= 180°

For second box - x=20

Explanation:

According to the given picture :-

We have ΔPQR having ∠P=(x)°, ∠Q= (3x)° and ∠R=(5x)°. (i)

To prove : x= 20

The angle sum property of triangle says that the total sum of all i terior angles of a triangle is 180°.

i.e. For ΔPQR

∠P+∠Q+∠R= 180° (ii)

Using substitution property , Substitute the values of ∠P, ∠Q and ∠R from (i) in (ii), we get

(x)°+(3x)°+(5x)°= 180°

⇒x+3x+5x=180 [Simplify]

⇒9x=180

Using division property of equality , divide both sides by 9 , we get\

x=20

hence, the completed proof is given below .