Question

lesson 19: evidence, angles, and proof

• lets make convincing explanations.

19.1: math talk: supplementary angles
mentally evaluate all of the missing angle measures in each figure.
figure a
figure b
figure c
figure d

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Calculate the missing angle in Figure A

Let the missing angle be \(x\). We know that \(x + 50^{\circ}=180^{\circ}\). So \(x = 180^{\circ}- 50^{\circ}=130^{\circ}\).

Step3: Calculate the missing angle in Figure B

Let the missing angle be \(y\). We know that \(y+30^{\circ}=180^{\circ}\). So \(y = 180^{\circ}-30^{\circ}=150^{\circ}\).

Step4: Calculate the missing angle in Figure C

Let the missing angle be \(z\). We know that \(z + 65^{\circ}=180^{\circ}\). So \(z=180^{\circ}-65^{\circ}=115^{\circ}\).

Step5: Calculate the missing angle in Figure D

Let the missing angle be \(w\). We know that \(w + 135^{\circ}=180^{\circ}\). So \(w=180^{\circ}-135^{\circ}=45^{\circ}\).

Answer:

Figure A: \(130^{\circ}\), Figure B: \(150^{\circ}\), Figure C: \(115^{\circ}\), Figure D: \(45^{\circ}\)