Question

Please help! Due In 2 minutes!

Answer 1

The measure of ∡a is 168° and that of ∡b is 12°.

What is the sum of three angles of a triangle?
The sum of three angles of a triangle is 180°, as available in mathematical literature.
What is the sum of two supplementary angles?
Two angles are referred to as supplementary angles if their combined value is 180°. A straight angle is created when supplementary angles are combined (180°).
In other words, ∡A and ∡B are supplementary if ∡A plus ∡B equals 180°. Angles A and B are described as "supplements" of one another in this context.
In math, A° + B° = 180°.

For the figure in question, since sum of three angles of a triangle = 180°
Thus, 78° + 90° + b° = 180°
b° = 180° - (90°+78°) = 12°
Again, from figure, ∡a and ∡b serve as supplementary angles, thus
a° + b° = 180° ⇒ a° = 180° - b° ⇒ a° = 168°
Therefore, m∡a = 168°, m∡b = 12°

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