In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?

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1 answer

To find the measure of \(\angle D\), we need to establish a relationship between \(\angle A\) and \(\angle D\). However, you didn't provide any additional information about their relationship such as whether they are congruent, supplementary, or part of a geometric figure like a triangle or quadrilateral.

Assuming \(\angle A\) and \(\angle D\) are supplementary (which is often the case in many problems), we can set up the equation:

\[ m\angle A + m\angle D = 180° \]

Substituting the expressions for the angles:

\[ (4x - 10) + (2x + 22) = 180 \]

Combine like terms:

\[ 6x + 12 = 180 \]

Now, solve for \(x\):

\[ 6x = 180 - 12 \] \[ 6x = 168 \] \[ x = 28 \]

Now, substitute \(x\) back into the expression for \(\angle D\):

\[ m\angle D = 2x + 22 \] \[ m\angle D = 2(28) + 22 \] \[ m\angle D = 56 + 22 \] \[ m\angle D = 78° \]

So, the measure of \(\angle D\) is \(78°\).