Question

find the measure of the angle indicated.
question 4
1 pts
solve for x:

Explanation:

First Problem (Find the measure of angle at E)

Step1: Recall quadrilateral angle sum

The sum of interior angles of a quadrilateral is \(360^\circ\). Let the measure of \(\angle E\) be \(x\).

Step2: Sum the known angles

Known angles: \(110^\circ\) (at D), \(70^\circ\) (at C), \(85^\circ\) (at F). Their sum is \(110 + 70 + 85 = 265^\circ\).

Step3: Solve for \(x\)

Using the angle - sum property: \(x+265 = 360\). So, \(x = 360 - 265=95^\circ\).

Step1: Identify the quadrilateral type

The quadrilateral \(VUTW\) has two pairs of equal angles (\(\angle V=\angle T = 106^\circ\), \(\angle U = 74^\circ\)), so it is a parallelogram. In a parallelogram, consecutive angles are supplementary. Also, opposite angles are equal, and we can also use the angle - sum property of a quadrilateral (sum of interior angles of a quadrilateral is \(360^\circ\)). Let's use the fact that consecutive angles in a parallelogram are supplementary or the angle - sum property. Let's use the angle - sum property. The sum of interior angles of a quadrilateral is \(360^\circ\). Let's sum the known angles and the angle \(13x - 4\).
The known angles are \(106^\circ\) (at V), \(74^\circ\) (at U), \(106^\circ\) (at T). Let the angle at W be \(13x - 4\).

Step2: Sum the known angles

Sum of known angles: \(106+74 + 106=286^\circ\)

Step3: Set up the equation

Using the angle - sum property of a quadrilateral: \((13x - 4)+286 = 360\)
Simplify the left - hand side: \(13x+282 = 360\)

Step4: Solve for \(x\)

Subtract 282 from both sides: \(13x=360 - 282 = 78\)
Divide both sides by 13: \(x=\frac{78}{13}=6\)

Answer:

\(95^\circ\)

Second Problem (Solve for \(x\))