In triangle ABC , the measure of angle A is 50 ^° . If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B ?

The correct answer is D. Choice D is correct. The sum of the three interior angles in a triangle is 180 ^° . It's given that angle A measures 50 ^° . If angle B measured 100 ^° , the measure of angle C would be 180 ^° - (50 ^° + 100 ^°) = 30 ^° . Thus, the measures of the angles in the triangle would be 50 ^° , 100 ^° , and 30 ^° . However, an isosceles triangle has two angles of equal measure. Therefore, angle B can't measure 100 ^° .

SAT Question 901e3285: Answer, Explanation & Desmos Solution

In triangle $A BC$ , the measure of angle $A$ is $5 0^{\circ}$ . If triangle $A BC$ is isosceles, which of the following is NOT a possible measure of angle $B$ ?

Difficulty:Medium

$5 0^{\circ}$

$6 5^{\circ}$

$8 0^{\circ}$

$10 0^{\circ}$

Explanation

Correct answer: D.

Choice D is correct. The sum of the three interior angles in a triangle is $18 0^{\circ}$ . It's given that angle $A$ measures $5 0^{\circ}$ . If angle $B$ measured $10 0^{\circ}$ , the measure of angle $C$ would be $18 0^{\circ} - (5 0^{\circ} + 10 0^{\circ}) = 3 0^{\circ}$ . Thus, the measures of the angles in the triangle would be $5 0^{\circ}$ , $10 0^{\circ}$ , and $3 0^{\circ}$ . However, an isosceles triangle has two angles of equal measure. Therefore, angle $B$ can't measure $10 0^{\circ}$ .

Desmos solution:

Note: The three possible isosceles configurations are checked: B = A (50°), B = C ((180-50)/2 = 65°), and C = A (180-2*50 = 80°). The value 100° does not appear in any valid case.

Enter in Desmos:

$\frac{180 - 50}{2}$
$180 - 2 \cdot 50$

Reviewed and rewritten by CookSAT

Why the other choices are wrong

Choice A

Choice A is incorrect. If angle $B$ has measure $5 0^{\circ}$ , then angle $C$ would measure $18 0^{\circ} - (5 0^{\circ} + 5 0^{\circ}) = 8 0^{\circ}$ , and $5 0^{\circ}$ , $5 0^{\circ}$ , and $8 0^{\circ}$ could be the angle measures of an isosceles triangle.

Choice B

Choice B is incorrect. If angle $B$ has measure $6 5^{\circ}$ , then angle $C$ would measure $18 0^{\circ} - (6 5^{\circ} + 5 0^{\circ}) = 6 5^{\circ}$ , and $5 0^{\circ}$ , $6 5^{\circ}$ , and $6 5^{\circ}$ could be the angle measures of an isosceles triangle.

Choice C

Choice C is incorrect. If angle $B$ has measure $8 0^{\circ}$ , then angle $C$ would measure $18 0^{\circ} - (8 0^{\circ} + 5 0^{\circ}) = 5 0^{\circ}$ , and $5 0^{\circ}$ , $8 0^{\circ}$ , and $5 0^{\circ}$ could be the angle measures of an isosceles triangle.

SAT Question 901e3285: Lines, Angles, and Triangles answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong