In the figure shown, r || s. If the measure of ∠ 2 = 146°, what is the measure of ∠ 7

Mathematics

1 answer:

borishaifa [10]2 years ago

3 0

Answer:

34°

Step-by-step explanation:

1. First, let's find the measure of ∠1 because since r || s, that means ∠1 = ∠7 because they're both alternate exterior angles. Alternate exterior angles are congruent.

2. (Solving for ∠1)

$146 + x = 180$
$146 + x - 146 = 180 - 146$
$x = 34$

3. Now, since we know ∠1 = ∠7, ∠7 = 34°.

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$x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.$