Yes; because ∠9 and ∠7 are vertical angles, m∠9 = 90°. Because ∠6 and ∠8 are complementary angles, m∠6 + m∠8 = 90°. Thus, m∠9 = m∠6 + m∠8.
In Mathematics, a complementary angle refers to two angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical expression:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
Based on vertical angles theorem, we can logically deduce that angle 7 and angle 9 are congruent angles. Also, a right angle represent 90 degrees;
m∠9 ≅ m∠7 = 90°
Furthermore, the sum of angles 6 and 8 are complementary angles;
m∠6 + m∠8 = 90°
m∠9 = m∠6 + m∠8 (Transitive property).
Complete Question:
Determine whether the statement can be assumed from the given figure. Explain.