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The measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle
The measure of the smaller interior angle is
and the measure of the larger interior angle is?

Respuesta :

clarch19

Answer:

smaller ∡ = 26°

larger ∡ = 154°

Step-by-step explanation:

opposite angles are congruent

adjacent angles are supplementary

in this problem, the angles are supplementary

'x' = measure of smaller angle

x + 50 + 4x = 180

5x = 130

x = 26

The given information and the relationship between the angles of a

parallelogram can be used to find the interior angles.

  • The measure of the smaller angle is 26°
  • The measure of the larger angle is 154°

Reasons:

A property of a parallelogram is that the diagonally opposite angles are

equal, and the adjacent angles are supplementary.

Therefore, two of the four interior angles of a parallelogram are equal.

Let x and y represent the two angles of different measure in the

parallelogram

y = 4·x + 50°

y + x = 180°

Which gives;

y = 180° - x

Therefore;

180° - x = 4·x + 50°

180° - 50° = 4·x + x

130° = 5·x

x = 130° ÷ 5 = 26°

  • x = 26°

y = 4 × 26° + 50° = 154°

  • y = 154°

Therefore;

  • The measure of the smaller interior angle, x = 26°
  • The measure of the larger interior angle, y = 154°

Learn more about the properties of a parallelogram here:

https://brainly.com/question/9793817

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