Question

Find the unknown in each of the following figures.

Answer 1

x+30+X+40+2x+10= 180°( Linear pair)

=}4x+80=180°

=}4x= 180°-80°=100°

=} x= 100/4=25°

Hence, the angles are:

x+30= 25+30= 55°

x+40= 25+40= 65°

2x+10=2(25)+10=50+10=60

[Check: 55+65+60=180°]

Hope it helps

Answer 2

Answer:

• ∠GED = 55°
• ∠GEH = 65°
• ∠HEF = 60°

Step-by-step explanation:

Given that:

• ∠GED = x + 30°
• ∠GEH = x + 40°
• ∠HEF = 2x + 10°

To Find:

• All the angles.

Process:

We have been provided the angles in the form of expressions here and we have to find the angles. As the angles are on a straight line, so the sum of all the angles is equal to 180° (linear pair). So, we can form an equation as:

• (x + 30°) + (x + 40°) + (2x + 10°) = 180°

After solving the equation and getting the value of x, we can substitute the values to respective expressions to get the values of the angles.

Solution:

$\sf{\implies (x+30)+(x+40)+(2x+10)=180}$

Opening the brackets,

$\sf{\implies x+30+x+40+2x+10=180}$

Solving further,

$\sf{\implies x+x+2x+30+40+10=180}$

$\sf{\implies 4x+80=180}$

Transposing 80 from LHS to RHS and changing its sign,

$\sf{\implies 4x=180-80}$

Subtracting,

$\sf{\implies 4x=100}$

Transposing 4 from LHS to RHS and changing its sign,

$\sf{\implies x=\dfrac{100}{4}}$

Dividing,

$\sf{\implies x=25}$

Hence,

• x = 25°

Therefore,

• ∠GED = x + 30° = 25° + 30° = 55°
• ∠GEH = x + 40° = 25° + 40° = 65°
• ∠HEF = 2x + 10° = 2 × 25° + 10° = 50° + 10° = 60°