Question

which of the following figures has an∠abc of 90 °? select an answer:

Explanation:

Step1: Recall the theorem

The angle inscribed in a semi - circle is a right - angle. That is, if \(AC\) is the diameter of the circle and \(B\) is a point on the circle, then \(\angle ABC = 90^{\circ}\).

Step2: Analyze each figure

Check if \(AC\) is the diameter and \(B\) lies on the circle for each option. In the first figure, \(AC\) is the diameter of the circle and \(B\) is a point on the circle, so \(\angle ABC=90^{\circ}\). In the second figure, \(B\) is not on the semi - circular arc subtended by the diameter \(AC\), so \(\angle ABC
eq90^{\circ}\). In the third figure, \(B\) is not on the semi - circular arc subtended by the diameter \(AC\), so \(\angle ABC
eq90^{\circ}\). In the fourth figure, \(B\) is not on the semi - circular arc subtended by the diameter \(AC\), so \(\angle ABC
eq90^{\circ}\).

Answer:

The first figure.