Question

for exercises 5 - 7, refer to the figure at the right. 5. identify two obtuse vertical angles. 6. identify two acute adjacent angles. 7. identify an angle supplementary to ∠tnu. 8. find the measures of two complementary angles if the difference in their measures is 18.

Explanation:

Step1: Recall angle - related definitions

Vertical angles are opposite each other when two lines intersect. Obtuse angles are angles between 90° and 180°. Adjacent angles share a common side and a common vertex. Supplementary angles add up to 180°. Complementary angles add up to 90°.

Step2: Answer question 5

Looking at the figure, if we assume some angle - measures based on the intersection of lines at point N, two obtuse vertical angles could be ∠RNV and ∠SNU (assuming they are obtuse).

Step3: Answer question 6

Two acute adjacent angles could be ∠VNT and ∠TNU (assuming they are acute).

Step4: Answer question 7

An angle supplementary to ∠TNU is ∠SNU since ∠TNU+∠SNU = 180° (linear - pair of angles).

Step5: Answer question 8

Let the two complementary angles be x and y. We know that x + y=90° (complementary angles) and x - y = 18°. Add the two equations: (x + y)+(x - y)=90 + 18. Simplifying gives 2x=108, so x = 54°. Substitute x = 54° into x + y=90°, we get 54+y = 90, then y=90 - 54=36°.

Answer:

1. ∠RNV and ∠SNU
2. ∠VNT and ∠TNU
3. ∠SNU
4. 54° and 36°