Question

1. in the diagrams shown below, fill in the measure of each missing angle. (a) 23° (b) 46° (c) 53°

Explanation:

Step1: Identify angle - type in (a)

The given angle in (a) is part of a right - angle which is 90°.

Step2: Calculate missing angle in (a)

Let the missing angle be $x$. Then $x = 90^{\circ}-23^{\circ}=67^{\circ}$.

Step3: Identify angle - type in (b)

The angles in (b) are supplementary (linear pair), and the sum of angles in a linear pair is 180°.

Step4: Calculate missing angle in (b)

Let the missing angle be $y$. Then $y = 180^{\circ}-46^{\circ}=134^{\circ}$.

Step5: Identify angle - type in (c)

The angles in (c) are vertical angles. Vertical angles are equal.

Step6: Calculate missing angle in (c)

The angle opposite to 53° (missing angle) is 53° due to vertical - angle property.

Answer:

(a) 67°
(b) 134°
(c) 53°