Question

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?
$60^\circ, 70^\circ, 50^\circ$
$circ$ yes
triangles with these measurements select
$circ$ no
(b) can these be the angle measures of a triangle?
$20^\circ, 105^\circ, 55^\circ$
$circ$ yes
triangles with these measurements

Explanation:

Step1: Sum the angles (a)

$60^\circ + 70^\circ + 50^\circ = 180^\circ$

Step2: Check triangle validity (a)

Since the sum equals $180^\circ$, a triangle is possible.

Step3: Check congruence (a)

Triangles with matching angles are similar, not necessarily congruent (sides can scale).

Step4: Sum the angles (b)

$20^\circ + 105^\circ + 55^\circ = 180^\circ$

Step5: Check triangle validity (b)

Since the sum equals $180^\circ$, a triangle is possible.

Step6: Check congruence (b)

Triangles with matching angles are similar, not necessarily congruent (sides can scale).

Answer:

(a) Yes; Triangles with these measurements are not all congruent
(b) Yes; Triangles with these measurements are not all congruent