In a quadrilateral ABCD, the acute angle A is greater than 30 degrees, and the other three angles
| June 10, 2021 | education
In a quadrilateral ABCD, the acute angle A is greater than 30 degrees, and the other three angles are equal. What values can the angle ABC take?
In order to solve this problem, you need to know the properties of the quadrangle and draw a picture to make it easier to understand the situation. If A> 30 °, then: 30 ° <A <90 °, the remaining three angles will remain less than 330 ° (but more than 270 °), because (the sum of the angles of a 4-gon = 360 °), then:
360 ° – 90 ° <B + C + D <360 ° – 30 °.
270 ° <3 * B <330 °.
90 ° <B <110 °.
Therefore, our answer is: 90 ° <B <110 °.
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