Question

if line cd is perpendicular to line EF m angle ECH = (x+5) and m angle HCD = (3x-7) find each missing value x= ECH HCD GCF ECG GCD

Answer 1

Answer:

$x = 23$

$ECH = 28$

$HCD = 62$

$GCF = 28$

$ECG = 152$

$GCD = 118$

Step-by-step explanation:

Given

$ECH = x + 5$

$HCD = 3x - 7$

Solving (a): The value of x

Since CD is perpendicular to EF, then the following relationship exists

$ECH + HCD = ECD$

Where ECD = 90° and DCF = 90°

Substitute values for ECH, HCD and ECD

$x + 5 + 3x - 7 = 90$

Collect like terms

$x + 3x = 90 + 7 - 5$

$4x = 92$

Divide both sides by 4

$x = 23$

Solving (b): The value of ECH

Given that

$ECH = x + 5$

Substitute 23 for x

$ECH = 23 + 5$

$ECH = 28$

Solving (c): The value of HCD

Given that

$HCD = 3x - 7$

Substitute 23 for x

$HCD = 3 * 23 - 7$

$HCD = 69 - 7$

$HCD = 62$

Solving (d): Solving GCF

GCF and ECH are opposites

Hence,

$GCF = ECH = 28$

Solving (e): The value of ECG

$ECG + ECH = 180$

Make ECG the subject of formula

$ECG = 180 - ECH$

Substitute 28 for ECH

$ECG = 180 - 28$

$ECG = 152$

Solving (f): The value of GCD

$GCD = GCF + DCF$

Recall that DCF = 90 and GCF = 28

$GCD = 90 + 28$

$GCD = 118$