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°

Verified 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 \(\sf x\) and then find the measures of the angles \(\sf \angle P\), \(\sf \angle K\), and \(\sf \angle M\).

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

\(\sf m/P + m/K + m/M = 180^\circ\)

Given:

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

So, we have:

\(\sf (11x - 10) + (7x + 3) + (12x + 7) = 180\)

Simplify and solve for \(\sf x\):

\(\sf 11x - 10 + 7x + 3 + 12x + 7 = 180\)

\(\sf 30x = 180\)

\(\sf x = 6\)

Now we substitute \(\sf x = 6\) back into the expressions for the angles:

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

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

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

Therefore, the true statements are:

  • \(\sf x = 6\)
  • \(\sf m/\angle P = 56^\circ\)
  • \(\sf m/\angle M = 79^\circ\)
  • \(\sf m/\angle K = 45^\circ\)

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