1. **Problem statement:** Given that PQ is parallel to MN, LRT is an isosceles triangle with LR = RT, and SLT is a straight line, find the value of $x$. 2. **Key facts and formulas:** - Alternate interior angles are equal when lines are parallel. - The sum of angles in a triangle is $180^\circ$. - In an isosceles triangle, the base angles are equal. - Angles on a straight line sum to $180^\circ$. 3. **Step-by-step solution:** - Since $PQ \parallel MN$, angle $0 = 22^\circ$ (given) is an alternate interior angle. - Triangle $LRT$ is isosceles with $LR = RT$, so base angles $L$ and $T$ are equal. - Given base angles $28^\circ$ each, sum of base angles is $28^\circ + 28^\circ = 56^\circ$. - Using triangle angle sum: $$a + 28 + 28 = 180 \implies a = 180 - 56 = 124^\circ$$ - Angle $b = 28^\circ$ (alternate interior angle). - Angle $L$ on the straight line $SLT$ is supplementary to $a$: $$L = 180 - 124 = 56^\circ$$ - Finally, $x$ is supplementary to $L$ on the straight line, so: $$x = 180 - 56 = 124^\circ$$ 4. **Answer:** The value of $x$ is $124^\circ$. This confirms your solution is correct.