Answered

APKM has m/P = (11x - 10)°, m/K = (7x+3)°,
and m/M= (12x+7)°. Using the given information,
select all the true statements.
x = 6
x = 5
m< P = 45°
m< P = 56°
m< M = 79°
m< M = 67°
m< K = 38°
m< K = 45°



Answer :

chibabykalu16

Answer:

x = 6

m< P = 56°

m< M = 79°

m< K = 45°

Step-by-step explanation:

To determine which statements are true, we need to solve for [tex] \sf x [/tex] and then find the measures of the angles [tex] \sf \angle P [/tex], [tex] \sf \angle K [/tex], and [tex] \sf \angle M [/tex].

First, let's calculate [tex] \sf x [/tex] by using the fact that the sum of the angles in a triangle is [tex] \sf 180^\circ [/tex]:

[tex] \sf m/P + m/K + m/M = 180^\circ [/tex]

Given:

  • [tex] \sf m/P = (11x - 10)^\circ [/tex]
  • [tex] \sf m/K = (7x + 3)^\circ [/tex]
  • [tex] \sf m/M = (12x + 7)^\circ [/tex]

So, we have:

[tex] \sf (11x - 10) + (7x + 3) + (12x + 7) = 180 [/tex]

Simplify and solve for [tex] \sf x [/tex]:

[tex] \sf 11x - 10 + 7x + 3 + 12x + 7 = 180 [/tex]

[tex] \sf 30x = 180 [/tex]

[tex] \sf x = 6 [/tex]

Now we substitute [tex] \sf x = 6 [/tex] back into the expressions for the angles:

[tex] \sf m/P = 11x - 10 = 11(6) - 10 = 66 - 10 = 56^\circ [/tex]

[tex] \sf m/K = 7x + 3 = 7(6) + 3 = 42 + 3 = 45^\circ [/tex]

[tex] \sf m/M = 12x + 7 = 12(6) + 7 = 72 + 7 = 79^\circ [/tex]

Therefore, the true statements are:

  • [tex] \sf x = 6 [/tex]
  • [tex] \sf m/\angle P = 56^\circ [/tex]
  • [tex] \sf m/\angle M = 79^\circ [/tex]
  • [tex] \sf m/\angle K = 45^\circ [/tex]

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