Help pls asap! Confused!

x = 13°

y = 36°

Step-by-step explanation:

Given the diagram of vertical angles, such that the sides of two angles form two pairs of opposite rays:

We are also given the following values for the following angles:

∠BMQ = (x + 10)°

∠DME = (3x - 16)°

∠EMQ = (5y - x - 10)°

According to the Vertical Angles Congruence Theorem, vertical angles are congruent.

In the given diagram, the following are vertical angles:

∠BMQ and ∠DME

∠BMD and ∠QME

Thus, in reference to the Vertical Angles Congruence Theorem, we can establish the following equality statement to solve for the value of x:

∠BMQ = ∠DME

(x + 10)° = (3x - 16)°

We can proceed to solve for the value of x. Start by adding 16° to both sides:

x° + 10° + 16° = 3x° - 16° + 16°

x° + 26° = 3x°

Next, subtract x° from both sides:

x° - x° + 26° = 3x° - x°

26° = 2x°

Divide both sides by 2° to solve for x:

By definition, linear pairs are two adjacent angles whose noncommon sides are the opposite rays. Linear pairs are also supplementary angles whose measures add up to 180°.

In the given diagram, the following angles are linear pairs:

∠DME and ∠EMQ

∠EMQ and ∠QMB

∠QMB and ∠BMD

∠BMD and ∠DME

Using the given value for ∠DME and ∠EMQ, we can solve for the value of y by setting up the following equation:

m∠DME + m∠EMQ = 180°  ⇒ By definition of Linear Pairs.

(3x - 16)° + (5y - x - 10)° = 180°

Substitute the value of x into the equation:

3(13)° - 16° + 5y° - 13° - 10° = 180°

Combine like terms:

39° - 16° + 5y° - 13° - 10° = 180°

0° + 5y° = 180°

5y° = 180°

Divide both sides by 5 to solve for y:

y = 36°

Verify whether we have the correct values for x and y by substituting their values into each angle:

Verify:  ∠BMQ and ∠DME are vertical angles with the same measure:

∠BMQ = (x + 10)° = 13° + 10° = 23°

∠DME = (3x - 16)° = 3(13)° - 16° = 23°

⇒ True statement.

m∠DME + m∠EMQ = 180°  ⇒ By definition of Linear Pairs.

∠DME = 23°

∠EMQ = (5y - x - 10)° = [5(36) - 13 - 10]° = 180 - 23 = 157°

23° + 157° = 180°

180° = 180° (True statement).

c

step-by-step explanation:

all teachers

step-by-step explanation: