Question

what are the values of a and p?
a = \boxed{\circ}
p = \boxed{\circ}
submit

Explanation:

Step1: Use linear pair for $a$

The angle $a$ and $a+40^\circ$ form a straight line, so their sum is $180^\circ$.
$$a + (a + 40^\circ) = 180^\circ$$
$$2a + 40^\circ = 180^\circ$$
$$2a = 180^\circ - 40^\circ$$
$$2a = 140^\circ$$
$$a = 70^\circ$$

Step2: Find triangle angles

First, calculate the third angle of the triangle:
$$a - 49^\circ = 70^\circ - 49^\circ = 21^\circ$$
We know $a = 70^\circ$, so the three angles of the triangle sum to $180^\circ$.
$$21^\circ + 70^\circ + (p - 3^\circ) = 180^\circ$$

Step3: Solve for $p$

Simplify the angle sum equation:
$$91^\circ + p - 3^\circ = 180^\circ$$
$$p + 88^\circ = 180^\circ$$
$$p = 180^\circ - 88^\circ$$
$$p = 92^\circ$$

Answer:

$a = 70^\circ$
$p = 92^\circ$