Question

question 5 module 8 lesson 1 - 3 graded decide whether it is possible for a triangle to have the three angle measures or three side lengths given. if it is possible, then decide whether all such triangles are congruent. (a) can these be the angle measures of a triangle? 116°, 62°, 123° yes triangles with these measurements must be congruent. no skip question

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate the sum of given angles

Sum \(= 116^\circ + 62^\circ + 123^\circ = 301^\circ\).

Step3: Compare with \(180^\circ\)

Since \(301^\circ
eq 180^\circ\), the angles can't form a triangle.

Answer:

No (and the initial "Yes" is incorrect because the sum of the angles \(116^\circ + 62^\circ + 123^\circ = 301^\circ\), which is not equal to \(180^\circ\), so a triangle with these angle measures is not possible.)