Since angles 1 and 2 together form a right angle, we know that m∠1 + m∠2 = 90°. Since m∠2 = 47°, we can substitute this value into the equation: m∠1 + 47° = 90°. To find m∠1, we can subtract 47° from both sides: m∠1 = 90° - 47° = 43°.
Now that we know m∠1 = 43°, we can find m∠4 by subtracting angles 1, 2, and 3 from a straight angle (180°). m∠4 = 180° - m∠1 - m∠2 - m∠3. We know that m∠1 = 43° and m∠2 = 47°. To find m∠3, we can subtract m∠1 + m∠2 from 90° (since angles 1 and 2 together form a right angle): m∠3 = 90° - m∠1 - m∠2 = 90° - 43° - 47° = 90° - 90° = 0°.
Now we can substitute these values into the equation for m∠4: m∠4 = 180° - m∠1 - m∠2 - m∠3 = 180° - 43° - 47° - 0° = 90°.
Therefore, m∠4 is 90°.
Use the image to answer the question.
An illustration shows five rays emerging from a point labeled A, forming the following angles from left to right: 1, 2, 3, 4, and 5. Angles 1 and 2 together form a right angle.
If m∠2=47° , what is m∠4 ?
(1 point)
1 answer