Question

1. find the values of x and y in the diagram below.

(4y - 18)°
(y + 14)°
(6x - 11)°
81°
(x + 5)°

1. in δmnp, if m∠m = (4x - 3)°, m∠n = (9x - 6)°, and m∠p = (6x - 1)°, find the value of x and the measure of each angle.

x =
m∠m =
m∠n =
m∠p =

Explanation:

Step1: Use Triangle Angle Sum Theorem

The sum of the interior angles of a triangle is \(180^\circ\). So, \(m\angle M + m\angle N + m\angle P = 180^\circ\). Substitute the given expressions: \((4x - 3) + (9x - 6) + (6x - 1) = 180\).

Step2: Simplify the Equation

Combine like terms: \(4x + 9x + 6x - 3 - 6 - 1 = 180\) → \(19x - 10 = 180\).

Step3: Solve for \(x\)

Add 10 to both sides: \(19x = 190\). Divide by 19: \(x = 10\).

Step4: Find \(m\angle M\)

Substitute \(x = 10\) into \(4x - 3\): \(4(10) - 3 = 37^\circ\).

Step5: Find \(m\angle N\)

Substitute \(x = 10\) into \(9x - 6\): \(9(10) - 6 = 84^\circ\).

Step6: Find \(m\angle P\)

Substitute \(x = 10\) into \(6x - 1\): \(6(10) - 1 = 59^\circ\).

Answer:

\(x = 10\)
\(m\angle M = 37^\circ\)
\(m\angle N = 84^\circ\)
\(m\angle P = 59^\circ\)