Question

1. find the measure of each missing angle.

35°
2
1
m∠1 =

m∠2 =

m∠3 =

m∠4 =

m∠5 =

Explanation:

Step1: Find \(m\angle1\)

Since the triangle with \(\angle1\) is a right - triangle and the two sides are equal (marked with the same tick), it is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle. So \(m\angle1 = 45^{\circ}\)

Step2: Find \(m\angle2\)

We know that the angle above \(\angle2\) is \(35^{\circ}\). The total angle along the vertical side (straight line concept in a non - parallel case here, but using the property of the figure's construction). \(m\angle2=90^{\circ}-35^{\circ}-45^{\circ}=10^{\circ}\)

Step3: Find \(m\angle5\)

Since the triangle with \(\angle1\) and \(\angle5\) is a right - triangle and two sides are equal (marked with the same tick), \(m\angle5 = 45^{\circ}\)

Step4: Find \(m\angle4\)

\(\angle4\) and \(\angle5\) form a linear pair. \(m\angle4 = 180^{\circ}-45^{\circ}=135^{\circ}\)

Step5: Find \(m\angle3\)

The large right - triangle (the whole figure). The sum of angles in a triangle is \(180^{\circ}\). One angle is \(90^{\circ}\), another is \(35^{\circ}\). Let's use the property of similar or related triangles (by side - tick marks, the two small triangles on the right have some relations). Also, using the angle sum property. \(m\angle3=180^{\circ}-90^{\circ}-35^{\circ}-10^{\circ}=45^{\circ}\)

Answer:

\(m\angle1 = 45^{\circ}\)
\(m\angle2 = 10^{\circ}\)
\(m\angle3 = 45^{\circ}\)
\(m\angle4 = 135^{\circ}\)
\(m\angle5 = 45^{\circ}\)