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# In the following figure, each pair of intersecting lines are perpendicular and the points of intersection are the midpoints of the lines.

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In the following figure, each pair of intersecting lines are perpendicular and the points of intersection are the midpoints of the lines. Also, DE = 14, BS = 20, MH = 26, GF = 25. Which is the length of SE + SM + GM + GF?

A. 52

B. 47

C. 45

D. 55

Lines AN and CT are perpendicular. If the measure of angle AFT is 3x + 21 and the measure of angle CFN is y + 45, which is the value of x + y?

A. 70

B. 40

C. 69

D. 68

In the following figure, line CG and HS are perpendicular.

Which is the measure of angle RDF?

A. 95

B. 65

C. 60

D. 75

Mar 9, 2020

### 1+0 Answers

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First  one

DE   =14  ....so SE   = 7

BS  = 20....so  SM   =10

MH  =26....so  GM   = 13

GF  = 25

So   SE + SM +  GM + GF  =

7 + 10  +  13  +  25  =

55

Second one

If  AN ad CT  are perpendicular....then  AFT  and   CFN  are right  angles

Which implies  that

3x + 21  = 90          and                       y  + 45   =  90

Subtract 21 from both sides                Subtract  45  from both sides

3x  = 69

Divide  both sides  by  3                        y  =  45

x  = 23

So   x  +  y  =   23  +  45   =  68

Last  one

The  sum of HDR  +  RDF  + SDF    = 180

So

55  +  HDR  + 30  =  180   simplify

HDR  +  85    =180           subtract  85 from  both sides

HDR   =  95

Mar 9, 2020