Two parallel lines $l$ and $m$ are cut by a transversal $t$ . If the interior angles of the same side of $t$ are $(2 x - 8)^{\circ}$ and $(3 x - 7)^{\circ}$ , find the measure of each of these angles.

Open in App

Solution

Using the property of interior angles on same sides
$\begin{matrix} 2 x - 8 + 3 x - 7 = 180 5 x - 15 = 180 x = 39^{\circ} 2 x - 8 = 2 \times 39 - 8 = 70 3 x - 7 = 3 \times 39 - 7 = 110 \end{matrix}$

Suggest Corrections

Similar questions

Two parallel lines $l$ and $m$ are cut by a transversal $t$ . If the interior angles on the same side of the transversal $t$ be $2 x - 9$ and $3 x - 7$ . Find the measure of each angle.

Q. Two parallel lines l and m are by a transversal t. If the interior angles of the same side of the be (2x-8)° and (3x-7)°,find the measure of each of these angles.

(a) Lines AB & CD are parallel and cut by a transversal t. List the alternate, corresponding, co-interior and vertically opposite angles.

(b) (i)

l and m are parallel lines and t is the transversal. Find x

(ii)

l and m are parallel lines and t is the transversal. Find x.
[4 MARKS]

Q. Which of the following statements are true (T) and which are false (F)? Give reasons.

(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two line parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Q. AP and BQ are the bisectors of two alternate interior angles formed by the intersection of a transversal t with parallel lines

l

and

m

. If

∠ P A B = x ∠ Q B A

. Find

x

Join BYJU'S Learning Program

Two parallel lines l and m are cut by a transversal t. If the interior angles of the same side of t are (2x−8)∘ and (3x−7)∘, find the measure of each of these angles.

Using the property of interior angles on same sides2x−8+3x−7=1805x−15=180x=39∘2x−8=2×39−8=703x−7=3×39−7=110

Two parallel lines $l$ and $m$ are cut by a transversal $t$ . If the interior angles of the same side of $t$ are $(2 x - 8)^{\circ}$ and $(3 x - 7)^{\circ}$ , find the measure of each of these angles.

Using the property of interior angles on same sides
$\begin{matrix} 2 x - 8 + 3 x - 7 = 180 5 x - 15 = 180 x = 39^{\circ} 2 x - 8 = 2 \times 39 - 8 = 70 3 x - 7 = 3 \times 39 - 7 = 110 \end{matrix}$