Using the provided diagram and angle measures, prove that PT is parallel to QS.

April 14, 2026Mathematics

ScanSolve AI Answer

April 14, 2026

Answer

Here's the solution to question 3:

a) Prove that $PT \parallel QS$

Step 1: Identify given parallel lines and angles. We are given that $PU \parallel QT$ . We are given the following angles: $\angle UPT = x$ $\angle QPT = x+40^\circ$ $\angle PQT = y$ $\angle QTS = 42^\circ$ $\angle RQS = 82^\circ$

Step 2: Use properties of parallel lines $PU \parallel QT$ . Since $PU \parallel QT$ and $PT$ is a transversal, the alternate interior angles are equal: $\angle UPT = \angle PTQ$

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QFind tan(x) and cos(x) in the diagram. Find sin(θ) and cos(θ) in the diagram. Find the value of Γ si…QExpress the following vectors graphically: A = (2cm, 35°), B = (4cm, 120°), C = (3cm, 210°)QFactorise the following completely: 1) 10x2 - 9xy + 2y2, 2) 5x2 + 18xy + 9y2 Q2 Mariam collects empty cans for recycling. She collects 3 cans on day 1, 6 cans on day 2, 12 cans o…QComplete the following table with common fraction, decimal fraction and percentage.

See all Mathematics questions →

Still have questions?

Quick Answer

Here's the solution to question 3: a) Prove that PT QS Step 1: Identify given parallel lines and angles.

Asked on April 14, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 14, 2026

Here's the solution to question 3: a) Prove that PT QS Step 1: Identify given parallel lines and angles. We are given that PU QT. We are given the following angles: UPT = x QPT = x+40^ PQT = y QTS = 42^ RQS = 82^ Step 2: Use properties of parallel lines PU QT. Since PU QT and PT is a transversal, the alternate interior angles are equal: UPT = PTQ PTQ