In this figure, ∠TER = 80°. What is the measure of ∠BET? What is the measure of ∠SET? (Hint: Observe that ∠REB is a straight angle. Hence, the degree measure of ∠REB = 180° of which 80° is covered by ∠TER.)
Answer
B, E and R are in one straight line. ∠TER = 80°, so ∠BET = 100°; and since ∠SER = 90°, ∠SET = 10°.
Step 1 — find ∠BET. B, E and R lie on one straight line, so ∠REB is a straight angle.
Step 2 — find ∠SET. The figure shows that ES stands at 90° from the line BR, that is ∠SER = 90°.
∠SET = ∠SER − ∠TER = 90° − 80° = 10°
Why no protractor is needed: once you know that a straight line means 180° and a square corner means 90°, the rest is only addition and subtraction. Angles on a straight line always add up to 180°.
Check it yourself: ∠BES = ∠BET − ∠SET = 100° − 10° = 90° ✔ — exactly the right angle shown in the figure.