Question

1. in the given figure, l || m and t is a transversal. find the measure of all angles, if ∠1 = 35°. 6. in the given figures, p || q and t is a transversal. find the measure of x in each of the following figures: (a) (b) (c) 7. in the given figure, l || m. find the value of x. 8. in the given figure, ab || cd. find the value of 10. find the value of y, if l || m.

Explanation:

Step1: Identify angle - relationships

Use properties of parallel lines and transversals.

Step2: For problem 5

Since \(l\parallel m\) and \(t\) is a transversal, if \(\angle1 = 35^{\circ}\), corresponding - angles are equal.

Step3: For problem 6(a)

If \(p\parallel q\) and \(t\) is a transversal, \(x\) and the \(31^{\circ}\) angle are alternate - interior angles, so \(x = 31^{\circ}\).

Step4: For problem 6(b)

If \(p\parallel q\) and \(t\) is a transversal, \(x\) and the \(56^{\circ}\) angle are corresponding angles, so \(x = 56^{\circ}\).

Step5: For problem 6(c)

If \(p\parallel q\) and \(t\) is a transversal, \(x\) and the \(46^{\circ}\) angle are alternate - exterior angles, so \(x = 46^{\circ}\).

Step6: For problem 7

Draw a line parallel to \(l\) and \(m\) through \(O\). The angles \(43^{\circ}\) and \(52^{\circ}\) can be used to find \(x\). The sum of the angles formed by the parallel lines and the transversals gives \(x=43^{\circ}+52^{\circ}=95^{\circ}\).

Step7: For problem 8

Since \(AB\parallel CD\), we can use angle - relationships. Let's assume we use the properties of parallel lines and transversals to find the angle related to \(x\). If we consider the given angles and the parallel lines, we find the value of \(x\) based on corresponding or alternate angles. But without a clear description of the angles related to \(x\) in the figure, we assume a standard parallel - line and transversal situation. If we consider the angles formed by the parallel lines and the transversals, we can find \(x\). For example, if there are corresponding or alternate angles given, we can equate them. Let's assume the angle related to \(x\) is such that \(x\) and a given angle are supplementary or equal based on parallel - line properties.

Answer:

1. Corresponding - angle values based on \(\angle1 = 35^{\circ}\)

6(a). \(x = 31^{\circ}\)
6(b). \(x = 56^{\circ}\)
6(c). \(x = 46^{\circ}\)

1. \(x = 95^{\circ}\)
2. Value of \(x\) based on parallel - line and transversal angle - relationships (needs more specific figure details for exact value)