Two angles with a common vertex are given, the corresponding sides of which

Two angles with a common vertex are given, the corresponding sides of which are perpendicular. One of them is 4 times less than the second. Find these corners.

Given:

angle AOB and angle BOС have a common side OB,

AO is perpendicular to the OС,

angle BOС = 4 * angle AOB.

Find the degree measures of the angles AOB and BOС -?

Decision:

1. Since AO is perpendicular to the OС, the AOC angle is straight, that is, the AOC angle = 90 degrees.

2. Angle AOC = angle AOB + angle BOC;

90 = angle AOB + 4 * angle AOB;

90 = angle AOB * (1 + 4);

90 = angle AOB * 5 (in order to find an unknown factor, you need to divide the product by a known factor);

angle AOB = 90: 5;

angle AOB = 18 degrees;

angle ВOС = 4 * 18 = 72 degrees.

Answer: 18 degrees; 72 degrees.