Questions: m angle A = square degrees

Transcript text: m \angle A=\square^{\circ}

Solution

Solution Steps

Step 1: Find the measure of angle H.

The sum of the interior angles of a quadrilateral is 360°. In quadrilateral FHJI, we have:

m∠F + m∠H + m∠J + m∠I = 360°

133° + m∠H + 71° + 80° = 360°

284° + m∠H = 360°

m∠H = 360° - 284°

m∠H = 76°

Step 2: Find the measure of angle I.

We are given that quadrilaterals FHJI and BCDE are similar. Since m∠J and m∠C are both 71°, the corresponding angles of the two figures must be congruent. Therefore, m∠I = m∠D. Likewise, m∠F and m∠B are corresponding angles, so m∠F = m∠B = 133°. Since m∠H = 76°, then m∠E = 76°. Since m∠F = 133°, then m∠B = 133°. We already found that m∠H = 76° so the corresponding angle m∠E = 76°. We are given m∠C = 71°, so the corresponding angle m∠J = 71°.

Step 3: Find the sum of the angles in BCDE

The sum of the interior angles of a quadrilateral is 360°. m∠B + m∠C + m∠D + m∠E = 360° 133° + 71° + m∠I + 76° = 360° 280° + m∠I = 360° m∠I = 80°