Mills Macdonald
02/03/2024 · Junior High School
\( \angle 1 \) and \( \angle 2 \) are complementary angles. If \( \mathrm{m} \angle 1=(2 x+23)^{\circ} \) and \( \mathrm{m} \angle 2=(4 x+25)^{\circ} \), then find the measure of \( \angle 2 \).
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Since \( \angle 1 \) and \( \angle 2 \) are complementary angles, we have the equation:
\[
\mathrm{m} \angle 1 + \mathrm{m} \angle 2 = 90^\circ
\]
Substituting the expressions for \( \mathrm{m} \angle 1 \) and \( \mathrm{m} \angle 2 \):
\[
(2x + 23) + (4x + 25) = 90
\]
Combining like terms:
\[
2x + 4x + 23 + 25 = 90
\]
This simplifies to:
\[
6x + 48 = 90
\]
Next, we isolate \( x \) by subtracting 48 from both sides:
\[
6x = 90 - 48
\]
\[
6x = 42
\]
Now, divide both sides by 6:
\[
x = 7
\]
Now that we have the value of \( x \), we can find the measure of \( \angle 2 \):
\[
\mathrm{m} \angle 2 = 4x + 25
\]
Substituting \( x = 7 \):
\[
\mathrm{m} \angle 2 = 4(7) + 25
\]
Calculating this gives:
\[
\mathrm{m} \angle 2 = 28 + 25 = 53
\]
Thus, the measure of \( \angle 2 \) is
\[
\boxed{53^\circ}
\]
Quick Answer
The measure of \( \angle 2 \) is \( 53^\circ \).
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