Hi there!
Let there be two angles, ∠A and ∠B, that are supplementary to each other. Therefore:
∠A + ∠B = 180°
We can assign ∠B to be the greater angle. Assume ∠A has a measure of x°.
∠A = x°
∠B = x° + 30°
The sum is equal to 180°, so:
x° + (x° + 30°) = 180°
Solve for x°.
2x° + 30° = 180°
2x° = 150°
x° = 75°
Thus, ∠A = 75°.
Since ∠B is 30°, greater:
∠B = 75° + 30° = 105°.
Answer:
Step-by-step explanation:
The Side-Angle-Side method cana only be used when information given shows that an included angle which is between two sides of a ∆, as well as the two sides of the ∆ are congruent to the included side and two sides of the other ∆.
Thus, since John already knows that and
, therefore, an additional information showing that the angle between
and
in ∆ABC is congruent to the angle between
and
in ∆DEF.
For John to prove that ∆ABC is congruent to ∆DEF using the Side-Angle-Side method, the additional information needed would be .
See attachment for the diagram that has been drawn with the necessary information needed for John to prove that ∆ABC is congruent to ∆DEF.
