The given statement " If a ray divides an angle into two complementary angles, then the original angle is not a right angle" is false.
As, Complementary angles are those in which sum of two angles add up to 90 degrees.
Now, let us consider two angles made by the ray is 'x' and 'y'. According to the question, the ray divides an angle into two complementary angles which means
In this case since the two angles formed after being divided by ray are complementary it means they add up to 90 degrees. And hence, the original angle should be a right angle.
Therefore, it is false to say that the original angle is not a right angle.
Answer: the answer is 4
Step-by-step explanation:
*see attachment for the complete diagram and what is required.
Answer:
✅ST = 7 m
✅SU = 8 m
✅m<R = 46°
✅m<Q = 75°
✅m<S = 59°
Step-by-step explanation:
Given that ∆PQR ≅ ∆STU, therefore, their corresponding sides and angles would be congruent to each other.
Thus:
<P ≅ <S, therefore, m<P = m<S = 59°
<Q ≅ <T, therefore, m<Q = m<T = 75°
<R ≅ <U, therefore, m<R = m<U.
PQ ≅ ST, therefore, PQ = ST
QR ≅ TU, therefore, QR = TU
PR ≅ SU, therefore, PR = SU
Let's find the measure of the following with the information we already know:
✅ST = PQ = 7 m
✅SU = PR = 8 m
✅m<R = 180 - (m<P + m<Q) (sum of ∆)
m<R = 180 - (59°+ 75°) (substitution)
m<R = 180 - 134
m<R = 46°
✅m<Q = m<T = 75°
✅m<S = m<P = 59°