Question

if these two figures are similar, what is the measure of the missing angle? 90° 110° 90° 70° ?

Explanation:

Step1: Recall similar figures property

Similar figures have congruent corresponding angles.

Step2: Identify corresponding angles

The first trapezoid has angles \(90^\circ\), \(110^\circ\), \(90^\circ\), \(70^\circ\). For the second similar trapezoid, the missing angle should correspond to the \(110^\circ\) (or we can also think about the fact that in similar polygons, corresponding angles are equal. Alternatively, since trapezoids (specifically right trapezoids here as two angles are \(90^\circ\)) that are similar will have their non - right angles corresponding. The first trapezoid has a \(110^\circ\) angle, so the missing angle in the second trapezoid (which is similar) should be equal to the corresponding angle in the first trapezoid. Also, we can check the angle sum: the sum of interior angles of a quadrilateral is \(360^\circ\). For the first quadrilateral: \(90 + 110+90 + 70=360\). For the second quadrilateral, let the missing angle be \(x\). Assuming the other angles (the two right angles and the \(70^\circ\) - like angle) are the same (since similar), so \(90 + x+90 + 70 = 360\), solving for \(x\): \(x=360-(90 + 90+70)=110\). But more simply, using similarity: corresponding angles are equal. So the missing angle is equal to the \(110^\circ\) angle (or the non - 90, non - 70 angle) in the first figure.

Answer:

\(110^\circ\)