Question

Angles DEF and GEH have the following measures: m∠DEF = (x − 18)°, m∠GEH = (3x + 4)° Part A: If angle DEF and angle GEH are complementary angles, find the value of x. Show every step of your work. (4 points) Part B: Use the value of x from Part A to find the measures of angles DEF and GEH. Show every step of your work. (4 points) Part C: Could the angles also be vertical angles? Explain. (4 points)

Answer 1

To find the value of x, set up an equation using the fact that angles DEF and GEH are complementary. Substitute the value of x into the expressions for angle measures DEF and GEH to find their values. Angles DEF and GEH cannot be vertical angles because they are not formed by intersecting lines.

Step-by-step explanation:

Part A: To find the value of x, we need to set up an equation using the fact that angles DEF and GEH are complementary. Complementary angles add up to 90 degrees, so we can write the equation: (x - 18) + (3x + 4) = 90. Simplifying, we get: 4x - 14 = 90. Adding 14 to both sides, we have: 4x = 104. Finally, dividing both sides by 4, we find: x = 26.

Part B: Now that we know the value of x is 26, we can substitute it back into the expressions for angle measures DEF and GEH to find their values. Angle DEF = (x - 18) = (26 - 18) = 8 degrees. Angle GEH = (3x + 4) = (3 * 26 + 4) = 82 degrees.

Part C: Vertical angles are formed by two intersecting lines and have equal measures. Since angles DEF and GEH are not formed by intersecting lines, they cannot be vertical angles.

Answer 2

Part A: To find the value of x, we need to set up an equation since angle DEF and angle GEH are complementary angles. Complementary angles add up to 90 degrees.

So we have the equation: (x - 18) + (3x + 4) = 90.

Simplifying this equation, we combine like terms: 4x - 14 = 90.

Then, we isolate x by adding 14 to both sides of the equation: 4x = 104.

Finally, we divide both sides by 4 to solve for x: x = 26.

Therefore, the value of x is 26.

Part B: Now that we have the value of x, we can find the measures of angles DEF and GEH.

To find the measure of angle DEF, we substitute x = 26 into the equation m∠DEF = (x - 18)°.

m∠DEF = (26 - 18)° = 8°.

Therefore, angle DEF measures 8 degrees.

To find the measure of angle GEH, we substitute x = 26 into the equation m∠GEH = (3x + 4)°.

m∠GEH = (3(26) + 4)° = (78 + 4)° = 82°.

Therefore, angle GEH measures 82 degrees.

Part C: The angles DEF and GEH cannot be vertical angles. Vertical angles are formed by the intersection of two lines and are congruent (have equal measures). In this case, angles DEF and GEH are not formed by the intersection of two lines, so they cannot be vertical angles.

I hope this helps! Let me know if you have any further questions.

Step-by-step explanation: