Solve the problem.
-A student is asked to construct a triangle that satisfies the following criteria. The sum of the first and second angles is 90° more than the measure of the third angle. If the measure of the third angle is subtracted from the
Measure of the second angle, the result is twice the measure of the first angle. Find the measure of each angle of
The triangle.
A)First angle is 30°, second angle is 105°, third angle is 45°
B)First angle is 28°, second angle is 105°, third angle is 43°
C)First angle is 34°, second angle is 107°, third angle is 39°
D)First angle is 36°, second angle is 101°, third angle is 43°

Question

Quizplus · Accepted Answer

Given the conditions, let's denote the first angle as $A$, the second angle as $B$, and the third angle as $C$. The conditions can be translated into the following equations:1. $A + B = C + 90$2. $B - C = 2A$3. $A + B + C = 180$ (since the sum of angles in a triangle is 180°)Solving these equations simultaneously, we find that $A = 30°$, $B = 105°$, and $C = 45°$, which matches option A.

Solve the Problem. -A Student Is Asked to Construct a Triangle That Satisfies