Question

4 from unit 1, lesson 15 which of these sets of angle - measures could be the 3 angles in a triangle? a 40°, 50°, 60° b 50°, 60°, 70° c 60°, 70°, 80° d 70°, 80°, 90° 5 from unit 1, lesson 14 lines ab and cd are parallel. find the measures of the following angles. explain your reasoning a. angle bcd b. angle ecf c. angle dcf

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Check option A

$40^{\circ}+50^{\circ}+60^{\circ}=150^{\circ}
eq180^{\circ}$

Step3: Check option B

$50^{\circ}+60^{\circ}+70^{\circ}=180^{\circ}$

Step4: Check option C

$60^{\circ}+70^{\circ}+80^{\circ}=210^{\circ}
eq180^{\circ}$

Step5: Check option D

$70^{\circ}+80^{\circ}+90^{\circ}=240^{\circ}
eq180^{\circ}$

For the parallel - lines problem:

Step1: Identify angle relationship for $\angle BCD$

Since $AB\parallel CD$ and $\angle ABC = 38^{\circ}$, $\angle BCD$ and $\angle ABC$ are alternate interior angles. Alternate interior angles are equal when two parallel lines are cut by a transversal. So $\angle BCD=38^{\circ}$.

Step2: Identify angle relationship for $\angle ECF$

$\angle ECF$ and $\angle ABC$ are vertical angles. Vertical angles are equal. So $\angle ECF = 38^{\circ}$.

Step3: Identify angle relationship for $\angle DCF$

$\angle DCF$ and $\angle ABC$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So $\angle DCF=38^{\circ}$.

Answer:

For the triangle - angle problem: B. $50^{\circ},60^{\circ},70^{\circ}$
For the parallel - lines problem:
a. $38^{\circ}$ (Alternate interior angles)
b. $38^{\circ}$ (Vertical angles)
c. $38^{\circ}$ (Corresponding angles)