Question

1. if ∠a = 50° & ∠e = 70°, what is the measure of... ∠b = ∠c = ∠d = ∠f = ∠g = ∠h =

Explanation:

Step1: Find \(\angle b\)

In the right - angled triangle, \(\angle a+\angle b = 90^{\circ}\) (complementary angles in a right - triangle). Given \(\angle a = 50^{\circ}\), then \(\angle b=90^{\circ}-\angle a\).
\(\angle b = 90^{\circ}-50^{\circ}=40^{\circ}\)

Step2: Find \(\angle c\)

Since the two lines are parallel, \(\angle c=\angle e\) (corresponding angles). Given \(\angle e = 70^{\circ}\), so \(\angle c = 70^{\circ}\)

Step3: Find \(\angle d\)

\(\angle c+\angle d = 180^{\circ}\) (linear pair). Since \(\angle c = 70^{\circ}\), then \(\angle d=180^{\circ}-\angle c\)
\(\angle d = 180^{\circ}-70^{\circ}=110^{\circ}\)

Step4: Find \(\angle f\)

\(\angle f\) and \(\angle c\) are vertical angles. So \(\angle f=\angle c\)
\(\angle f = 70^{\circ}\)

Step5: Find \(\angle g\)

\(\angle g\) and \(\angle d\) are vertical angles. So \(\angle g=\angle d\)
\(\angle g = 110^{\circ}\)

Step6: Find \(\angle h\)

\(\angle h\) and \(\angle b\) are vertical angles. So \(\angle h=\angle b\)
\(\angle h = 40^{\circ}\)

Answer:

\(\angle b = 40^{\circ}\), \(\angle c = 70^{\circ}\), \(\angle d = 110^{\circ}\), \(\angle f = 70^{\circ}\), \(\angle g = 110^{\circ}\), \(\angle h = 40^{\circ}\)