Question

1. $m\angle nad = 138^\circ$ and $m\angle eah = 88^\circ$. find $m\angle nae$.

solve
a) $58^\circ$ b) $50^\circ$
c) $115^\circ$ d) $226^\circ$
6.
find the value of $\angle a$.
a) $25^\circ$ b) $30^\circ$
c) $35^\circ$ d) $90^\circ$
9.

Explanation:

Question 5

Step1: Analyze angle relationships

We know that \( m\angle NAD = 138^\circ \) and \( m\angle EAH = 88^\circ \). Wait, maybe there's a typo, but assuming a straight angle or complementary/supplementary. Wait, maybe the diagram has a right angle? Wait, no, let's re - check. Wait, maybe \( \angle NAD \) and \( \angle NAE \) and \( \angle EAH \) have a relationship. Wait, perhaps \( m\angle NAE=m\angle NAD - m\angle EAD \)? Wait, no, maybe the correct approach is: If we assume that there is a straight line or a right angle, but let's recalculate. Wait, \( 138 - 88 = 50 \)? Wait, no, \( 138-88 = 50 \)? Wait, \( 138 - 88=50 \)? Wait, no, \( 138 - 88 = 50 \)? Wait, maybe the angle \( \angle NAE=m\angle NAD - m\angle EAH \) (if they are related by a common vertex). So \( 138 - 88 = 50^\circ \)? Wait, no, \( 138-88 = 50 \)? Wait, \( 138 - 88=50 \), so \( m\angle NAE = 50^\circ \)? Wait, no, maybe I made a mistake. Wait, let's think again. If \( \angle NAD \) is \( 138^\circ \) and \( \angle EAH \) is \( 88^\circ \), and they share a common part, then \( \angle NAE=\angle NAD-\angle EAD \), but if \( \angle EAD \) is \( 88^\circ \), then \( 138 - 88 = 50 \). So the answer is \( 50^\circ \), which is option b.

Step2: Verify the calculation

\( m\angle NAE=138^\circ - 88^\circ=50^\circ \)

Step1: Identify the right angle

The diagram shows a right angle (the square corner) which is \( 90^\circ \), and there is a \( 65^\circ \) angle. The angle \( \angle A \) is \( 90^\circ-65^\circ \)

Step2: Calculate \( \angle A \)

\( \angle A = 90^\circ - 65^\circ=25^\circ \)

Step1: Analyze the angles on a straight line

The angles on a straight line sum up to \( 180^\circ \). We have angles \( 60^\circ \), \( 120^\circ \) and the angle with line \( EG \). Wait, the question is probably about verifying if they are supplementary. \( 60^\circ+120^\circ = 180^\circ \), so they are supplementary (form a linear pair). But if the question is to find something else, but from the diagram, \( \angle DEG = 60^\circ \) and \( \angle GEF = 120^\circ \), and \( 60 + 120=180 \), so they are supplementary. But since the question is not fully stated, but if we assume to check if they are supplementary, \( 60^\circ+120^\circ = 180^\circ \), so they form a linear pair.

Answer:

b) \( 50^\circ \)

Question 6