Question

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


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Btw its not 78 got it

Answer 1

To find the measure of \( \angle D \), you'll need to set up an equation involving both angles \( \angle A \) and \( \angle D \) since they are expressed in terms of \( x \).

If you know that \( \angle A \) and \( \angle D \) are related in a specific way (such as supplementary or equal), you can use that information to solve for \( x \). However, without additional information, let's assume \( \angle A \) and \( \angle D \) are equal:

\[
m\angle A = m\angle D
\]

This gives us the equation:

\[
4x - 10 = 2x + 22
\]

Now, solve for \( x \):

1. Subtract \( 2x \) from both sides:

\[
4x - 2x - 10 = 22
\]

This simplifies to:

\[
2x - 10 = 22
\]

2. Add 10 to both sides:

\[
2x = 32
\]

3. Divide both sides by 2:

\[
x = 16
\]

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

\[
m\angle D = 2x + 22 = 2(16) + 22 = 32 + 22 = 54^\circ
\]

Thus, the measure of \( \angle D \) is \( 54^\circ \).