Question

question 24 of 40
a triangle has angles a, b, and c. which of the following could not be a set of angles?
a. $m\angle a = 46^\circ$, $m\angle b=90^\circ$, $m\angle c = 46^\circ$
b. $m\angle a = 47^\circ$, $m\angle b=91^\circ$, $m\angle c = 42^\circ$
c. $m\angle a = 99^\circ$, $m\angle b=51^\circ$, $m\angle c = 30^\circ$
d. $m\angle a = 45^\circ$, $m\angle b=90^\circ$, $m\angle c = 45^\circ$

Explanation:

Step1: Recall triangle angle sum rule

The sum of interior angles of a triangle is $180^\circ$.

Step2: Calculate sum for Option A

$46^\circ + 90^\circ + 46^\circ = 182^\circ$

Step3: Calculate sum for Option B

$47^\circ + 91^\circ + 42^\circ = 180^\circ$

Step4: Calculate sum for Option C

$99^\circ + 51^\circ + 30^\circ = 180^\circ$

Step5: Calculate sum for Option D

$45^\circ + 90^\circ + 45^\circ = 180^\circ$

Step6: Identify invalid set

Only Option A's sum is not $180^\circ$.

Answer:

A. $m\angle A = 46^\circ, m\angle B=90^\circ, m\angle C = 46^\circ$