Since angles 1 and 2 together form a right angle, angle 2 is a complementary angle to angle 1. This means that the measure of angle 1 plus the measure of angle 2 equals 90 degrees. Therefore, the measure of angle 1 is 90 - 47 = 43 degrees.
Since angles 3, 4, and 5 are consecutive angles, they add up to 180 degrees. This means that the measure of angle 3 plus the measure of angle 4 plus the measure of angle 5 equals 180 degrees. Therefore, the measure of angle 4 is 180 - (47 + 43) = 90 degrees.
Therefore, m∠4 = 90 degrees.
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)
°
3 answers
Use the image to answer the question.
An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?
(2 points)
x°+°=°
An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?
(2 points)
x°+°=°
Based on the image and the information given, we can see that angle 5 and angle 8 are corresponding angles. Corresponding angles are congruent if the two lines being intersected by the slanting line are parallel. Therefore, we can set up an equation using the congruence of angle 5 and angle 8.
m∠5 = m∠8
112° = (2x + 8)°
To find x, we can solve for it by isolating the variable on one side of the equation. Let's subtract 8 from both sides of the equation:
104° = 2x°
Now, divide both sides of the equation by 2:
52° = x°
Therefore, the equation x + 52 = 0 will solve for x.
m∠5 = m∠8
112° = (2x + 8)°
To find x, we can solve for it by isolating the variable on one side of the equation. Let's subtract 8 from both sides of the equation:
104° = 2x°
Now, divide both sides of the equation by 2:
52° = x°
Therefore, the equation x + 52 = 0 will solve for x.
1 answer