1. **Problem:** Given $m(\angle A) = 70^\circ$ and $\angle A$ is complementary to $\angle B$, find the measure of $\angle B$. 2. **Formula:** Complementary angles sum to $90^\circ$. 3. **Calculation:** $$m(\angle B) = 90^\circ - m(\angle A) = 90^\circ - 70^\circ = 20^\circ$$ 4. **Answer:** $\angle B = 20^\circ$. --- 1. **Problem:** Find the sum of interior angles of a triangle. 2. **Rule:** The sum of interior angles in any triangle is always $180^\circ$. 3. **Answer:** $180^\circ$. --- 1. **Problem:** Given two sides of a triangle are 5 cm and 6 cm, find the possible length of the third side. 2. **Rule:** The triangle inequality states the third side $x$ must satisfy: $$|5 - 6| < x < 5 + 6$$ $$1 < x < 11$$ 3. **Answer:** Among the options, $4$ satisfies this condition. --- 1. **Problem:** Find the sum of interior angles of a quadrilateral. 2. **Rule:** The sum of interior angles of an n-sided polygon is: $$180^\circ \times (n-2)$$ For $n=4$: $$180^\circ \times 2 = 360^\circ$$ 3. **Answer:** $360^\circ$. --- 1. **Problem:** If the diagonals of a parallelogram are equal, identify the shape. 2. **Rule:** A parallelogram with equal diagonals is a rectangle. 3. **Answer:** Rectangle. --- 1. **Problem:** Find the number of axes of symmetry of an isosceles triangle. 2. **Rule:** An isosceles triangle has exactly 1 axis of symmetry. 3. **Answer:** 1. --- 1. **Problem:** Determine the quadrant of the point $(-2, 3)$. 2. **Rule:** Quadrants are defined as: - Quadrant I: $(+,+)$ - Quadrant II: $(-,+)$ - Quadrant III: $(-,-)$ - Quadrant IV: $(+,-)$ 3. **Answer:** Since $x=-2$ (negative) and $y=3$ (positive), the point lies in Quadrant II. --- 1. **Problem:** If the point $(-2k, 2k+3)$ lies on the $y$-axis, find $k$. 2. **Rule:** Points on the $y$-axis have $x=0$. 3. **Calculation:** $$-2k = 0 \Rightarrow k = 0$$ 4. **Answer:** $k=0$ (Note: None of the options match 0, so possibly a typo in options.) --- 1. **Problem:** Given midpoint $M(5,3)$ of segment $AB$ with $A(x,4)$ and $B(1,6)$, find $x$. 2. **Formula:** Midpoint coordinates: $$M_x = \frac{x + 1}{2} = 5$$ 3. **Calculation:** $$x + 1 = 10 \Rightarrow x = 9$$ 4. **Answer:** $x=9$ (Note: None of the options match 9, so possibly a typo in options.)