Question

8 Here is a parallelogram.
(2x + 43)degrees
(5x – 20)degrees
(4y - 5x)degrees
Work out the value of x and the value of y.

Answer 1

Answer:

y = 50°  ||  x = 21°

Explanation:

• parallelogram is a quadrilateral with two pairs of parallel sides

solve for x:

→ 2x + 43 = 5x - 20

• [ group variables ]

→ 2x - 5x = -20 - 43

• [ simplify ]

→ -3x = -63

• [ divide both sides by -3 ]

→ x = 21°

total interior angle of 4 sides shape is 360°

"so when all angles sum up"

Find y from:

→ 4y -5x + 4y -5x + 2x + 43 + 5x - 20 = 360°

• [ replace 21° with x ]

→ 4y -5(21) + 4y -5(21) + 2(21) + 43 + 5(21) - 20 = 360°

• [ simplify ]

→ 8y - 40° = 360°

→ 8y = 360° + 40°

→ 8y = 400°

• [ divide both sides by 8 ]

→ y = 50°

Answer 2

Opposite angles of parallelogram are equal

$\\ \tt\hookrightarrow 5x-20=2x+43$

$\\ \tt\hookrightarrow 3x=63$

$\\ \tt\hookrightarrow x=21$

Now

Consecutive angles have sum 180°

$\\ \tt\hookrightarrow 5x-20+4y-5x=180$

$\\ \tt\hookrightarrow 4y-20=180$

$\\ \tt\hookrightarrow 4y=200$

$\\ \tt\hookrightarrow y=50$